{"id":6022,"date":"2023-07-23T05:38:13","date_gmt":"2023-07-23T05:38:13","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6022"},"modified":"2023-07-23T05:44:59","modified_gmt":"2023-07-23T05:44:59","slug":"ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5"},"content":{"rendered":"<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 10 Maths\u00a0<\/span><\/strong><br \/>\n<strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 3 (Pair of Linear Equations in Two Variables)\u00a0<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 10 Mathematics <strong>Chapter &#8211; 3 Pair of Linear Equations in Two Variables <\/strong>Exercise 3.5 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #ff0000;\"><strong>Chapter : 3 Pair of Linear Equations in Two Variables<\/strong> <\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-1\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 3.1<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-2\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 3.2<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-3\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 3.3<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-4\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 3.4<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-6\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 3.6<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-7\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 3.7<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 3.5<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Which of the following pairs of linear equations has a unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using the cross-multiplication method.<br \/>\n<\/strong><strong>(i) x \u2013 3y \u2013 3 = 0<br \/>\n3x \u2013 9y \u2013 2 = 0 <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 2x + y = 5<br \/>\n3x + 2y = 8<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) 3x \u2013 5y = 20<br \/>\n6x \u2013 10y = 40 <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) x \u2013 3y \u2013 7 = 0<br \/>\n3x \u2013 3y \u2013 15 = 0<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solutions &#8211; <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) x \u2013 3y \u2013 3 = 0<br \/>\n3x \u2013 9y \u2013 2 = 0<br \/>\n<\/strong><sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/> <\/sub>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{-9}\" alt=\"\\frac{-3}{-9}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/>, \u00a0\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/><sub>\u00a0<\/sub>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{-2}\" alt=\"\\frac{-3}{-2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{2}\" alt=\"\\frac{3}{2}\" align=\"absmiddle\" \/><br \/>\n<sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/> <\/sub>\u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/> \u2260 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/><br \/>\nTherefore, the given sets of lines are parallel to each other. Therefore, they will not intersect each other and thus, there will not be any solution for these equations.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 2x + y = 5<br \/>\n3x + 2y = 8<br \/>\n<\/strong><sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/><\/sub> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{-8}\" alt=\"\\frac{-5}{-8}\" align=\"absmiddle\" \/><br \/>\n<sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/><\/sub>\u00a0 \u2260 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/><br \/>\nTherefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations. <\/span><br \/>\n<span style=\"color: #000000;\">By cross-multiplication method,<\/span><br \/>\n<span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{b_1c_2-c_1b_2}&amp;space;=&amp;space;\\frac{y}{c_1a_2&amp;space;-&amp;space;c_2a_1}&amp;space;=&amp;space;\\frac{1}{a_1b_2-a_2b_1}\" alt=\"\\frac{x}{b_1c_2-c_1b_2} = \\frac{y}{c_1a_2 - c_2a_1} = \\frac{1}{a_1b_2-a_2b_1}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{(-8-(-10))}=\\frac{y}{-15-(-16)}=\\frac{1}{4-3}\" alt=\"\\frac{x}{(-8-(-10))}=\\frac{y}{-15-(-16)}=\\frac{1}{4-3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{2}&amp;space;=&amp;space;\\frac{y}{1}\" alt=\"\\frac{x}{2} = \\frac{y}{1}\" align=\"absmiddle\" \/> = 1<br \/>\n\u2234 x = 2 and y =1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) 3x \u2013 5y = 20<br \/>\n6x \u2013 10y = 40<br \/>\n<\/strong><sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/><\/sub> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{6}\" alt=\"\\frac{3}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{-10}\" alt=\"\\frac{-5}{-10}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{20}{40}\" alt=\"\\frac{20}{40}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/> <\/sub>\u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/> =\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Therefore, the given sets of lines will be overlapping each other i.e., the lines will be coincident to each other and thus, there are infinite solutions possible for these equations.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) x \u2013 3y \u2013 7 = 0<br \/>\n3x \u2013 3y \u2013 15 = 0<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/><\/sub> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{-3}\" alt=\"\\frac{-3}{-3}\" align=\"absmiddle\" \/> = 1,\u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{-15}\" alt=\"\\frac{-7}{-15}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/><\/sub>\u00a0 \u2260 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/><br \/>\nTherefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations. <\/span><br \/>\n<span style=\"color: #000000;\">By cross-multiplication method,<\/span><br \/>\n<span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{b_1c_2-c_1b_2}&amp;space;=&amp;space;\\frac{y}{c_1a_2&amp;space;-&amp;space;c_2a_1}&amp;space;=&amp;space;\\frac{1}{a_1b_2-a_2b_1}\" alt=\"\\frac{x}{b_1c_2-c_1b_2} = \\frac{y}{c_1a_2 - c_2a_1} = \\frac{1}{a_1b_2-a_2b_1}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{45-21}&amp;space;=&amp;space;\\frac{y}{-21-(-15)}&amp;space;=&amp;space;\\frac{1}{-3-(-9)}\" alt=\"\\frac{x}{45-21} = \\frac{y}{-21-(-15)} = \\frac{1}{-3-(-9)}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{24}=\\frac{y}{-6}=\\frac{1}{6}\" alt=\"\\frac{x}{24}=\\frac{y}{-6}=\\frac{1}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{24}&amp;space;=&amp;space;\\frac{1}{6}\" alt=\"\\frac{x}{24} = \\frac{1}{6}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{y}{-6}&amp;space;=&amp;space;\\frac{1}{6}\" alt=\"\\frac{y}{-6} = \\frac{1}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2234 x = 4 and y = 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. (i) For which values of a and b do the following pair of linear equations have an infinite number of solutions?<br \/>\n<\/strong><strong>2x + 3y = 7<br \/>\n<\/strong><strong>(a \u2013 b) x + (a + b) y = 3a + b \u2013 2 <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) For which value of k will the following pair of linear equations have no solution?<br \/>\n<\/strong><strong>3x + y = 1<br \/>\n<\/strong><strong>(2k \u2013 1) x + (k \u2013 1) y = 2k + 1<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) <\/strong>2x + 3y &#8211; 7 =0<br \/>\n(a &#8211; b)x + (a + b)y \u2013 (3a + b -2) = 0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/><\/sub> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{a-b}\" alt=\"\\frac{2}{a-b}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{a+b}\" alt=\"\\frac{3}{a+b}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{-(3a&amp;space;+&amp;space;b&amp;space;-2)}\" alt=\"\\frac{-7}{-(3a + b -2)}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{(3a&amp;space;+&amp;space;b&amp;space;-2)}\" alt=\"\\frac{7}{(3a + b -2)}\" align=\"absmiddle\" \/><br \/>\nFor infinitely many solutions,<br \/>\n<sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/> <\/sub>\u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/> =\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Thus,<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{a-b}\" alt=\"\\frac{2}{a-b}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{(3a&amp;space;+&amp;space;b&amp;space;-2)}\" alt=\"\\frac{7}{(3a + b -2)}\" align=\"absmiddle\" \/><br \/>\n6a + 2b \u2013 4 = 7a \u2013 7b<br \/>\na \u2013 9b = -4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026. (i)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{a-b}\" alt=\"\\frac{2}{a-b}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{a+b}\" alt=\"\\frac{3}{a+b}\" align=\"absmiddle\" \/><br \/>\n2a + 2b = 3a \u2013 3b<br \/>\na \u2013 5b = 0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.\u2026. (ii)<br \/>\nSubtracting (i) from (ii), we get<br \/>\n(a \u2013 9b) &#8211; (a \u2013 5b) = &#8211; 4<br \/>\n&#8211; 4b = &#8211; 4<br \/>\nb =1<br \/>\nSubstituting this eq. in (ii), we get<br \/>\na &#8211; 5 \u00d7 1 = 0<br \/>\na = 5<br \/>\nThus, at a = 5 and b = 1, the given equations will have infinite solutions.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 3x + y -1 = 0<br \/>\n(2k &#8211; 1)x\u00a0 +\u00a0 (k &#8211; 1)y \u2013 2k &#8211; 1 = 0<br \/>\n<\/strong><sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/><\/sub> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{2k&amp;space;-&amp;space;1}\" alt=\"\\frac{3}{2k - 1}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{k-1}\" alt=\"\\frac{1}{k-1}\" align=\"absmiddle\" \/>,\u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{-2k-1}\" alt=\"\\frac{-1}{-2k-1}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2k&amp;space;+&amp;space;1}\" alt=\"\\frac{1}{2k + 1}\" align=\"absmiddle\" \/><br \/>\nFor no solutions,<br \/>\n<sub><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}\" alt=\"\\frac{a_1}{a_2}\" align=\"absmiddle\" \/> <\/sub>\u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{b_1}{b_2}\" alt=\"\\frac{b_1}{b_2}\" align=\"absmiddle\" \/> \u2260 \u00a0<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c_1}{c_2}\" alt=\"\\frac{c_1}{c_2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{2k&amp;space;-&amp;space;1}\" alt=\"\\frac{3}{2k - 1}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{k-1}\" alt=\"\\frac{1}{k-1}\" align=\"absmiddle\" \/> \u2260 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2k&amp;space;+&amp;space;1}\" alt=\"\\frac{1}{2k + 1}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{2k&amp;space;-&amp;space;1}\" alt=\"\\frac{3}{2k - 1}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{k-1}\" alt=\"\\frac{1}{k-1}\" align=\"absmiddle\" \/>\u00a0 \u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">3k &#8211; 3 = 2k -1<br \/>\nk =2<br \/>\nTherefore, for k = 2, the given pair of linear equations will have no solution.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. Solve the following pair of linear equations by the substitution and cross-multiplication methods.<br \/>\n<\/strong><strong>8x + 5y = 9<br \/>\n<\/strong><strong>3x + 2y = 4<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong>8x + 5y = 9 \u2026\u2026\u2026\u2026\u2026\u2026\u2026.. (i)<br \/>\n3x + 2y = 4 \u2026\u2026\u2026\u2026\u2026\u2026.\u2026. (ii)<br \/>\nFrom equation (ii), we get<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4-2y}{3}\" alt=\"\\frac{4-2y}{3}\" align=\"absmiddle\" \/> \u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026. (iii)<br \/>\nUsing this value in equation (i), we get<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8(4-2y)}{3}\" alt=\"\\frac{8(4-2y)}{3}\" align=\"absmiddle\" \/> + 5y = 9<br \/>\n32 \u2013 16y + 15y = 27<br \/>\n-y = -5<br \/>\ny = 5\u00a0 \u00a0 \u00a0 \u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026. (iv)<br \/>\nUsing this value in equation (ii), we get<br \/>\n3x + 10 = 4<br \/>\nx = -2<br \/>\nThus, x = -2 and y = 5<br \/>\nNow, using the Cross-multiplication method,<br \/>\n8x +5y \u2013 9 = 0<br \/>\n3x + 2y \u2013 4 = 0<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{-20+18}&amp;space;=&amp;space;\\frac{y}{-27+32}&amp;space;=&amp;space;\\frac{1}{16-15}\" alt=\"\\frac{x}{-20+18} = \\frac{y}{-27+32} = \\frac{1}{16-15}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-x}{2}&amp;space;=&amp;space;\\frac{y}{5}&amp;space;=\\frac{1}{1}\" alt=\"\\frac{-x}{2} = \\frac{y}{5} =\\frac{1}{1}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000;\">\u2234 x = -2 and y =5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) A part of monthly hostel charges is fixed, and the remaining depends on the number of days one has taken food in a mess. When student A takes food for 20 days, she has to pay Rs.1,000 as hostel charges, whereas student B, who takes food for 26 days, pays Rs.1,180 as hostel charges. Find the fixed charges and the cost of food per day. <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) A fraction becomes 1\/3 when 1 is subtracted from the numerator, and it becomes 1\/4 when 8 is added to its denominator. Find the fraction. <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) Yash scored 40 marks on a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test? <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and its breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solutions &#8211; <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) <\/strong>Let <i>x<\/i> be the fixed charge of the food and <i>y<\/i> be the charge for food per day.<\/span><br \/>\n<span style=\"color: #000000;\">According to the question,<br \/>\nx + 20y = 1000\u00a0 \u2026\u2026\u2026\u2026\u2026\u2026.. (i)<br \/>\nx + 26y = 1180\u00a0 \u00a0\u2026\u2026\u2026\u2026\u2026\u2026.. (ii)<br \/>\nSubtracting (i) from\u00a0 (ii), we get<br \/>\n(x + 26y) &#8211; (x + 20y) = 1180 &#8211; 1000<br \/>\n6y = 180<br \/>\ny = Rs.30<br \/>\nUsing this value in equation (ii), we get<br \/>\nx = 1180 &#8211; 26 \u00d7 30<br \/>\nx = 400<br \/>\nTherefore, the fixed charge is Rs.400, and the charge per day is Rs.30.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii)\u00a0<\/strong>Let the fraction be x\/y.<br \/>\nSo, as per the question given,<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(x-1)}{y}\" alt=\"\\frac{(x-1)}{y}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/><br \/>\n3x \u2013 y = 3\u00a0 \u00a0 \u2026\u2026\u2026\u2026\u2026\u2026\u2026 (i)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{(y+8)}\" alt=\"\\frac{x}{(y+8)}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{4}\" alt=\"\\frac{1}{4}\" align=\"absmiddle\" \/><br \/>\n4x \u2013 y = 8\u00a0 \u00a0 \u00a0 \u2026\u2026\u2026\u2026\u2026\u2026.. (ii)<br \/>\nSubtracting equation (i) from (ii), we get<br \/>\n(4x \u2013 y) &#8211; (3x \u2013 y) = 8 &#8211; 3<br \/>\nx = 5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u2026\u2026\u2026\u2026\u2026. (iii)<br \/>\nUsing this value in equation (ii), we get<br \/>\n(4 \u00d7 5) \u2013 y = 8<br \/>\ny = 12<br \/>\nTherefore, the fraction is 5\/12.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii)<\/strong> Let the number of right answers be x and the number of wrong answers be y.<br \/>\nAccording to the given question,<br \/>\n3x \u2212 y = 40\u00a0 \u00a0 \u2026\u2026.. (i)<br \/>\n4x \u2212 2y = 50<br \/>\n2x \u2212 y = 25\u00a0 \u2026\u2026.\u00a0 \u00a0 (ii)<br \/>\nSubtracting equation (ii) from equation (i), we get<br \/>\n(3x \u2212 y) &#8211; (2x \u2212 y) = 40 &#8211; 25<br \/>\nx = 15\u00a0 \u00a0 \u00a0\u2026.\u2026. (iii)<br \/>\nPutting this in equation (ii), we obtain<br \/>\n30 \u2013 y = 25<br \/>\ny = 5<br \/>\nTherefore, number of right answers = 15 and number of wrong answers = 5<br \/>\nHence, the total number of questions = 20<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv)<\/strong> Let x km\/h be the speed of the car from point A and y km\/h be the speed of the car from point B.<br \/>\nIf the car travels in the same direction,<br \/>\n5x \u2013 5y = 100<br \/>\nx \u2013 y = 20\u00a0 \u00a0 \u00a0 \u2026\u2026\u2026\u2026\u2026\u2026 (i)<br \/>\nIf the car travels in the opposite direction,<br \/>\nx + y = 100\u00a0 \u2026\u2026\u2026\u2026\u2026\u2026 (ii)<br \/>\nSolving equations (i) and (ii), we get<br \/>\n(x \u2013 y) + (x + y) = 20 + 100<br \/>\n2x = 120<br \/>\nx = 60\u00a0 \u00a0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026 (iii)<br \/>\nUsing this in equation (i), we get<br \/>\n60 \u2013 y = 20<br \/>\ny = 40<br \/>\nTherefore, the speed of the car from point A = 60 km\/h<br \/>\nSpeed of car from point B = 40 km\/h<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) <\/strong>Let, The length of the rectangle = x unit<br \/>\nAnd the breadth of the rectangle = y unit<br \/>\nNow, as per the question given,<br \/>\n(x \u2013 5) (y + 3) = xy &#8211; 9<br \/>\nxy + 3x \u2013 5y \u2013 15 = xy &#8211; 9<br \/>\n3x \u2013 5y \u2013 6 = 0\u00a0 \u00a0 \u00a0 \u00a0 \u2026\u2026\u2026\u2026\u2026\u2026 (i)<br \/>\n(x + 3) (y + 2) = xy + 67<br \/>\nxy + 2x + 3y + 6 = xy + 67<br \/>\n2x + 3y \u2013 61 = 0\u00a0 \u00a0 \u2026\u2026\u2026\u2026\u2026.. (ii)<br \/>\nUsing cross multiplication method, we get<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{305+18}=&amp;space;\\frac{y}{-12+183}=\\frac{1}{9+10}\" alt=\"\\frac{x}{305+18}= \\frac{y}{-12+183}=\\frac{1}{9+10}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{323}&amp;space;=&amp;space;\\frac{y}{171}&amp;space;=&amp;space;\\frac{1}{19}\" alt=\"\\frac{x}{323} = \\frac{y}{171} = \\frac{1}{19}\" align=\"absmiddle\" \/><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{323}&amp;space;=\\frac{1}{19}\" alt=\"\\frac{x}{323} =\\frac{1}{19}\" align=\"absmiddle\" \/>\u00a0 and\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{y}{171}&amp;space;=\\frac{1}{19}\" alt=\"\\frac{y}{171} =\\frac{1}{19}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000;\">Therefore, x = 17 and y = 9<br \/>\nHence, the length of the rectangle = 17 units<br \/>\nAnd the breadth of the rectangle = 9 units<\/span><\/p>\n<p><span style=\"font-family: Georgia, Palatino;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths\/\"><span style=\"color: #0000ff;\"><b><i>Go Back To Chapters<\/i><\/b><\/span><\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 10 Maths\u00a0 Chapter &#8211; 3 (Pair of Linear Equations in Two Variables)\u00a0 The NCERT Solutions in English Language for Class 10 Mathematics Chapter &#8211; 3 Pair of Linear Equations in Two Variables Exercise 3.5 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 3 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1043],"tags":[1045,1058,1063,1044,1049,1048],"class_list":["post-6022","post","type-post","status-publish","format-standard","hentry","category-class-10-maths","tag-class-10-ncert-mathematics-solutions","tag-ncert-class-10-mathematics-chapter-3-pair-of-linear-equations-in-two-variables-solutions","tag-ncert-class-10-mathematics-exercise-3-5-solutions","tag-ncert-class-10-mathematics-solutions-class-10-ncert-solutions","tag-ncert-solutions-class-10-mathematics","tag-ncert-solutions-class-10-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 10 Maths\u00a0Chapter - 3 (Pair of Linear Equations in Two Variables)\u00a0The NCERT Solutions in English Language for Class 10 Mathematics Chapter - 3 Pair of Linear Equations in Two Variables Exercise 3.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 3.5\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions Class 10 Maths\u00a0Chapter - 3 (Pair of Linear Equations in Two Variables)\u00a0The NCERT Solutions in English Language for Class 10 Mathematics Chapter - 3 Pair of Linear Equations in Two Variables Exercise 3.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 3.5\" \/>\n<meta property=\"og:url\" content=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/\" \/>\n<meta property=\"og:site_name\" content=\"TheExamPillar NCERT\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-23T05:38:13+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-07-23T05:44:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/latex.codecogs.com\/gif.latex?fraca_1a_2\" \/>\n<meta name=\"author\" content=\"Admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@exampillar\" \/>\n<meta name=\"twitter:site\" content=\"@exampillar\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"24 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/\"},\"author\":{\"name\":\"Admin\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#\\\/schema\\\/person\\\/521fbdbd2eb8621382a3096b5e3ecaf1\"},\"headline\":\"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5\",\"datePublished\":\"2023-07-23T05:38:13+00:00\",\"dateModified\":\"2023-07-23T05:44:59+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/\"},\"wordCount\":1151,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#\\\/schema\\\/person\\\/521fbdbd2eb8621382a3096b5e3ecaf1\"},\"image\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/latex.codecogs.com\\\/gif.latex?\\\\frac{a_1}{a_2}\",\"keywords\":[\"Class 10 NCERT Mathematics Solutions\",\"NCERT Class 10 Mathematics\u00a0Chapter - 3 Pair of Linear Equations in Two Variables Solutions\",\"NCERT Class 10 Mathematics Exercise 3.5 Solutions\",\"NCERT Class 10 Mathematics Solutions Class 10 NCERT Solutions\",\"NCERT Solutions Class 10 Mathematics\",\"NCERT Solutions Class 10 Maths\"],\"articleSection\":[\"Class 10 Maths\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/\",\"url\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/\",\"name\":\"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 | TheExamPillar NCERT\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/latex.codecogs.com\\\/gif.latex?\\\\frac{a_1}{a_2}\",\"datePublished\":\"2023-07-23T05:38:13+00:00\",\"dateModified\":\"2023-07-23T05:44:59+00:00\",\"description\":\"NCERT Solutions Class 10 Maths\u00a0Chapter - 3 (Pair of Linear Equations in Two Variables)\u00a0The NCERT Solutions in English Language for Class 10 Mathematics Chapter - 3 Pair of Linear Equations in Two Variables Exercise 3.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 3.5\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/#primaryimage\",\"url\":\"https:\\\/\\\/latex.codecogs.com\\\/gif.latex?\\\\frac{a_1}{a_2}\",\"contentUrl\":\"https:\\\/\\\/latex.codecogs.com\\\/gif.latex?\\\\frac{a_1}{a_2}\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#website\",\"url\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/\",\"name\":\"TheExamPillar NCERT\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#\\\/schema\\\/person\\\/521fbdbd2eb8621382a3096b5e3ecaf1\"},\"alternateName\":\"NCERT Solution\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":[\"Person\",\"Organization\"],\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#\\\/schema\\\/person\\\/521fbdbd2eb8621382a3096b5e3ecaf1\",\"name\":\"Admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2022\\\/07\\\/cropped-ExamPillar-PNG.png\",\"url\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2022\\\/07\\\/cropped-ExamPillar-PNG.png\",\"contentUrl\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2022\\\/07\\\/cropped-ExamPillar-PNG.png\",\"width\":512,\"height\":512,\"caption\":\"Admin\"},\"logo\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2022\\\/07\\\/cropped-ExamPillar-PNG.png\"},\"sameAs\":[\"https:\\\/\\\/theexampillar.com\\\/ncert\"],\"url\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/author\\\/ncert_eng_vikram\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 | TheExamPillar NCERT","description":"NCERT Solutions Class 10 Maths\u00a0Chapter - 3 (Pair of Linear Equations in Two Variables)\u00a0The NCERT Solutions in English Language for Class 10 Mathematics Chapter - 3 Pair of Linear Equations in Two Variables Exercise 3.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 3.5","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5","og_description":"NCERT Solutions Class 10 Maths\u00a0Chapter - 3 (Pair of Linear Equations in Two Variables)\u00a0The NCERT Solutions in English Language for Class 10 Mathematics Chapter - 3 Pair of Linear Equations in Two Variables Exercise 3.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 3.5","og_url":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/","og_site_name":"TheExamPillar NCERT","article_published_time":"2023-07-23T05:38:13+00:00","article_modified_time":"2023-07-23T05:44:59+00:00","og_image":[{"url":"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}","type":"","width":"","height":""}],"author":"Admin","twitter_card":"summary_large_image","twitter_creator":"@exampillar","twitter_site":"@exampillar","twitter_misc":{"Written by":"Admin","Est. reading time":"24 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/#article","isPartOf":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/"},"author":{"name":"Admin","@id":"https:\/\/theexampillar.com\/ncert\/#\/schema\/person\/521fbdbd2eb8621382a3096b5e3ecaf1"},"headline":"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5","datePublished":"2023-07-23T05:38:13+00:00","dateModified":"2023-07-23T05:44:59+00:00","mainEntityOfPage":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/"},"wordCount":1151,"commentCount":0,"publisher":{"@id":"https:\/\/theexampillar.com\/ncert\/#\/schema\/person\/521fbdbd2eb8621382a3096b5e3ecaf1"},"image":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/#primaryimage"},"thumbnailUrl":"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}","keywords":["Class 10 NCERT Mathematics Solutions","NCERT Class 10 Mathematics\u00a0Chapter - 3 Pair of Linear Equations in Two Variables Solutions","NCERT Class 10 Mathematics Exercise 3.5 Solutions","NCERT Class 10 Mathematics Solutions Class 10 NCERT Solutions","NCERT Solutions Class 10 Mathematics","NCERT Solutions Class 10 Maths"],"articleSection":["Class 10 Maths"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/","url":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/","name":"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 | TheExamPillar NCERT","isPartOf":{"@id":"https:\/\/theexampillar.com\/ncert\/#website"},"primaryImageOfPage":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/#primaryimage"},"image":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/#primaryimage"},"thumbnailUrl":"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}","datePublished":"2023-07-23T05:38:13+00:00","dateModified":"2023-07-23T05:44:59+00:00","description":"NCERT Solutions Class 10 Maths\u00a0Chapter - 3 (Pair of Linear Equations in Two Variables)\u00a0The NCERT Solutions in English Language for Class 10 Mathematics Chapter - 3 Pair of Linear Equations in Two Variables Exercise 3.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 3.5","breadcrumb":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/#primaryimage","url":"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}","contentUrl":"https:\/\/latex.codecogs.com\/gif.latex?\\frac{a_1}{a_2}"},{"@type":"BreadcrumbList","@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-5\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/theexampillar.com\/ncert\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5"}]},{"@type":"WebSite","@id":"https:\/\/theexampillar.com\/ncert\/#website","url":"https:\/\/theexampillar.com\/ncert\/","name":"TheExamPillar NCERT","description":"","publisher":{"@id":"https:\/\/theexampillar.com\/ncert\/#\/schema\/person\/521fbdbd2eb8621382a3096b5e3ecaf1"},"alternateName":"NCERT Solution","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/theexampillar.com\/ncert\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":["Person","Organization"],"@id":"https:\/\/theexampillar.com\/ncert\/#\/schema\/person\/521fbdbd2eb8621382a3096b5e3ecaf1","name":"Admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/cropped-ExamPillar-PNG.png","url":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/cropped-ExamPillar-PNG.png","contentUrl":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/cropped-ExamPillar-PNG.png","width":512,"height":512,"caption":"Admin"},"logo":{"@id":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/cropped-ExamPillar-PNG.png"},"sameAs":["https:\/\/theexampillar.com\/ncert"],"url":"https:\/\/theexampillar.com\/ncert\/author\/ncert_eng_vikram\/"}]}},"_links":{"self":[{"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/posts\/6022","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/comments?post=6022"}],"version-history":[{"count":5,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/posts\/6022\/revisions"}],"predecessor-version":[{"id":6274,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/posts\/6022\/revisions\/6274"}],"wp:attachment":[{"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/media?parent=6022"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/categories?post=6022"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/tags?post=6022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}