{"id":4256,"date":"2023-02-05T05:44:38","date_gmt":"2023-02-05T05:44:38","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4256"},"modified":"2023-02-05T05:45:53","modified_gmt":"2023-02-05T05:45:53","slug":"ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-2\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.2"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 4 (Linear Equations in Two Variables)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Mathematics\u00a0<strong>Chapter &#8211; 4 Linear Equations in Two Variables <\/strong>Exercise 4.2 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter 4: Linear Equations in Two Variables<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-1\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 4.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-3\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 4.3<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-4-linear-equations-in-two-variables-ex-4-4\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 4.4<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 4.2\u00a0<\/span><\/h2>\n<p><span style=\"color: #000000;\"><strong>1. Which one of the following options is true, and why?<br \/>\n<\/strong><strong>y = 3x + 5 has<br \/>\n<\/strong><strong>(i) <\/strong>A unique solution<br \/>\n<strong>(ii) <\/strong>Only two solutions<strong><br \/>\n<\/strong><strong>(iii) <\/strong>Infinitely many solutions<br \/>\n<strong>Answer &#8211; <\/strong>Let us substitute different values for x in the linear equation y = 3x + 5<\/span><\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered\" style=\"width: 32.1314%;\">\n<tbody>\n<tr>\n<td style=\"width: 9.52381%;\"><span style=\"color: #000000;\"><strong>x<\/strong><\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">0<\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">1<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #000000;\">\u2026.<\/span><\/td>\n<td style=\"width: 13.8288%;\"><span style=\"color: #000000;\">100<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.52381%;\"><span style=\"color: #000000;\"><strong>y<\/strong><\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">5<\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">11<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">14<\/span><\/td>\n<td style=\"width: 16.6667%;\"><span style=\"color: #000000;\">\u2026.<\/span><\/td>\n<td style=\"width: 13.8288%;\"><span style=\"color: #000000;\">305<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><span style=\"color: #000000;\">From the table, it is clear that x can have infinite values, and for all the infinite values of x, there are infinite values of y as well.<br \/>\nHence, <strong>(iii) infinitely many solutions<\/strong> is the only option true.<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>2. Write four solutions for each of the following equations:<br \/>\n<\/strong><strong>(i) 2x + y = 7<br \/>\n(ii) \u03c0x + y = 9<br \/>\n(iii) x = 4y<br \/>\n<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong><strong>(i) 2x + y = 7<br \/>\n<\/strong>y = 7 &#8211; 2x<br \/>\nThen,<br \/>\n<\/span><\/p>\n<table class=\"table table-bordered\" style=\"width: 32.1314%;\">\n<tbody>\n<tr>\n<td style=\"width: 9.52381%;\"><span style=\"color: #000000;\"><strong>x<\/strong><\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">0<\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">1<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">3<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.52381%;\"><span style=\"color: #000000;\"><strong>y<\/strong><\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">7<\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">5<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">3<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #000000;\">The solutions are (0, 7), (1,5), (3,1), (2,3)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii) \u03c0x + y = 9<br \/>\n<\/strong>y = 9 &#8211; \u03c0x<\/span><\/p>\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td style=\"width: 9.52381%;\"><span style=\"color: #000000;\"><strong>x<\/strong><\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">0<\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">1<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">-1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.52381%;\"><span style=\"color: #000000;\"><strong>y<\/strong><\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">9<\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">9 &#8211; \u03c0<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">9 &#8211; 2\u03c0<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">9 + \u03c0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #000000;\">The solutions are (0, 9), (1, 9 &#8211; \u03c0), (2, 9 &#8211; \u03c0), (-1, 9 + \u03c0)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii) x = 4y<br \/>\n<\/strong>y = x\/4<\/span><\/p>\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td style=\"width: 9.52381%;\"><span style=\"color: #000000;\"><strong>x<\/strong><\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">0<\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">4<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">12<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 9.52381%;\"><span style=\"color: #000000;\"><strong>y<\/strong><\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">0<\/span><\/td>\n<td style=\"width: 11.1111%;\"><span style=\"color: #000000;\">1<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"width: 7.14285%;\"><span style=\"color: #000000;\">3<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #000000;\">The solutions are (0, 0), (4, 1), (8, 2), (12, 3)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>3. Check which of the following are solutions of the equation x \u2013 2y = 4 and which are not:<br \/>\n<\/strong><strong>(i) (0, 2)<br \/>\n<\/strong><strong>(ii) (2, 0)<br \/>\n<\/strong><strong>(iii) (4, 0)<br \/>\n<\/strong><strong>(iv) (\u221a2, 4\u221a2)<br \/>\n<\/strong><strong>(v) (1, 1)<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Answer &#8211;<\/strong><br \/>\n<strong>(i) (0, 2)<br \/>\n<\/strong>(x, y) = (0, 2)<br \/>\nPuffing x = 0 and y = 2 in x \u2013 2y = 4, we get<br \/>\n<strong>L.H.S.<\/strong><br \/>\n\u21d2 0 \u2013 2(2)<br \/>\n\u21d2 -4<br \/>\n<strong>R.H.S. <\/strong>= 4<br \/>\n\u2234 L.H.S. \u2260 R.H.S.<br \/>\n(0, 2) is <strong>not<\/strong> a solution of the equation x \u2013 2y = 4<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii) (2, 0)<br \/>\n<\/strong>(x, y) = (2, 0)<br \/>\nPutting x = 2 and y = 0 in x \u2013 2y = 4, we get<br \/>\n<strong>L.H.S. <\/strong><br \/>\n\u21d2 2 \u2013 2(0)<br \/>\n\u21d2 2 \u2013 0<br \/>\n\u21d2 2<br \/>\n<strong>R.H.S.<\/strong> = 4<br \/>\n\u2234 L.H.S. \u2260 R.H.S.<br \/>\n(2, 0) is\u00a0<strong>not<\/strong> a solution of the equation x &#8211; 2y = 4<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii) (4, 0)<br \/>\n<\/strong>(x, y) = (4, 0)<br \/>\nPutting x = 4 and y = o in x \u2013 2y = 4, we get<br \/>\n<strong>L.H.S.<\/strong><br \/>\n\u21d2 4 \u2013 2(0)<br \/>\n\u21d2 4 \u2013 0<br \/>\n\u21d2 4<br \/>\n<strong>R.H.S.<\/strong> = 4<br \/>\n\u2234 L.H.S. = R.H.S.<br \/>\n(4, 0) is <strong>a solution<\/strong> of the equation x \u2013 2y = 4<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iv) (\u221a2, 4\u221a2)<br \/>\n<\/strong>(x, y) = (\u221a2, 4\u221a2)<br \/>\nPutting x = \u221a2 and y = 4\u221a2 in x \u2013 2y = 4, we get<br \/>\n<strong>L.H.S.<\/strong><br \/>\n\u21d2 \u221a2 \u2013 2(4\u221a2)<br \/>\n\u21d2 \u221a2 \u2013 8\u221a2<br \/>\n\u21d2 -7\u221a2<br \/>\n<strong>R.H.S.<\/strong> = 4<br \/>\n\u2234 L.H.S. \u2260 R.H.S.<br \/>\n(\u221a2, 4\u221a2) is <strong>not<\/strong>\u00a0a solution of the equation x\u20132y = 4<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(v) (1, 1)<br \/>\n<\/strong>(x, y) = (1, 1)<br \/>\nPutting x = 1 and y = 1 in x \u2013 2y = 4, we get<br \/>\n<strong>LH.S. <\/strong><br \/>\n\u21d2 1 \u2013 2(1)<br \/>\n\u21d2 1 \u2013 2<br \/>\n\u21d2 -1<br \/>\n<strong>R.H.S <\/strong>= 4<br \/>\n\u2234 LH.S. \u2260 R.H.S.<br \/>\n(1, 1) is\u00a0<strong>not<\/strong> a solution of the equation x \u2013 2y = 4<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>4. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.<br \/>\n<\/strong><strong>Answer &#8211; <\/strong>We have 2x + 3y = k<br \/>\nputting x = 2 and y = 1 in 2x + 3y = k, we get<br \/>\n2(2) + 3(1)<br \/>\n\u21d2 k = 4 + 3 \u2013 k<br \/>\n\u21d2 7 = k<br \/>\nThus, the required value of k is 7.<\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Maths\u00a0 Chapter &#8211; 4 (Linear Equations in Two Variables)\u00a0 The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter &#8211; 4 Linear Equations in Two Variables Exercise 4.2 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 4: Linear Equations in Two Variables NCERT [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[707,702,186,708,701,5],"class_list":["post-4256","post","type-post","status-publish","format-standard","hentry","category-class-9-maths","tag-class-9th-chapter-4-linear-equations-in-two-variables-in-english","tag-ncert-solution-class-9","tag-ncert-solutions","tag-ncert-solutions-class-9-maths-chapter-4-in-english","tag-ncert-solutions-class-9-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - 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