{"id":6018,"date":"2023-07-22T07:22:36","date_gmt":"2023-07-22T07:22:36","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6018"},"modified":"2023-07-23T05:46:04","modified_gmt":"2023-07-23T05:46:04","slug":"ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-3-pair-of-linear-equations-in-two-variables-ex-3-1\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"font-family: Georgia, Palatino;\"><strong><span style=\"color: #000000;\">NCERT Solutions Class 10 Maths\u00a0<\/span><\/strong><\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\"><strong><span style=\"color: #000000;\">Chapter &#8211; 3 (Pair of Linear Equations in Two Variables)\u00a0<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">The NCERT Solutions in English Language for Class 10 Mathematics <strong>Chapter &#8211; 3 Pair of Linear Equations in Two Variables <\/strong>Exercise 3.1 has been provided here to help the students in solving the questions from this exercise.<\/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-3-2\/\" 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-3-5\/\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 3.5<\/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;\"><span style=\"font-family: Georgia, Palatino;\"><strong><span style=\"color: #000000;\">Exercise &#8211; 3.1\u00a0<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>1. Aftab tells his daughter, \u201cSeven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.\u201d (Isn\u2019t this interesting?) Represent this situation algebraically and graphically.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino;\"><span style=\"color: #000000;\"><strong>Solutions &#8211;<br \/>\n<\/strong><\/span>Let the present age of Aftab be \u2018x\u2019.<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">And, the present age of his daughter be \u2018y\u2019.<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">Now, we can write, seven years ago,<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">Age of Aftab = x &#8211; 7<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">Age of his daughter = y &#8211; 7<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">According to the question,<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x \u2212 7 = 7(y \u2212 7)<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x \u2212 7 = 7y \u2212 49<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x \u2212 7y = \u221242\u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8212;&#8212;&#8212;&#8212;&#8212;- (i)<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">Also, three years from now or after three years,<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">Age of Aftab will become = x + 3.<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">Age of his daughter will become = y + 3<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">According to the situation given,<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x + 3 = 3(y + 3)<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x + 3 = 3y + 9<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x \u2212 3y = 6\u00a0 \u00a0 \u00a0&#8212;&#8212;&#8212;&#8212;&#8212;&#8211; (ii)<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">Subtracting equation (i) from equation (ii) we have<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">(x \u2212 3y) \u2212 (x \u2212 7y) = 6 \u2212 (\u221242)<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">\u22123y + 7y = 6 + 42<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">4y = 48<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">y = 12<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">The algebraic equation is represented by<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x \u2212 7y = \u221242<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x \u2212 3y = 6<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">For, x \u2212 7y = \u221242<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x = \u221242+7y<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">The solution table is<\/span><\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">x<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">-7<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">7<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">y<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">7<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-family: Georgia, Palatino;\">For, \u00a0x \u2212 3y = 6<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">x = 6 + 3y<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\">The solution table is<\/span><\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">x<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">y<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">0<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">-1<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">-2<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-family: Georgia, Palatino;\">The graphical representation is:<\/span><br \/>\n<span style=\"font-family: Georgia, Palatino;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6170\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que1.png\" alt=\"NCERT Class 10 Maths Solution\" width=\"654\" height=\"664\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que1.png 654w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que1-295x300.png 295w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que1-300x305.png 300w\" sizes=\"auto, (max-width: 654px) 100vw, 654px\" \/><\/span><\/p>\n<p><span style=\"font-family: Georgia, Palatino;\"><span style=\"color: #000000;\"><strong>2. The coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later, she buys another bat and 3 more balls of the same kind for Rs.1300. Represent this situation algebraically and geometrically.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>Solutions &#8211; <\/strong>Let us assume that the cost of a bat be Rs \u2018x\u2019<br \/>\n<\/span><span style=\"color: #000000;\">And, the cost of a ball be Rs \u2018y\u2019<br \/>\n<\/span><span style=\"color: #000000;\">According to the question, the algebraic representation is<br \/>\n<\/span><span style=\"color: #000000;\">3x + 6y = 3900\u00a0 &#8212;&#8212;&#8212;&#8212;&#8211; (i)<br \/>\nx + 3y = 1300\u00a0 &#8212;&#8212;&#8212;&#8212;&#8211; (ii)<br \/>\n<\/span><span style=\"color: #000000;\">For 3x + 6y = 3900<br \/>\n<\/span><span style=\"color: #000000;\">x + 2y = 1300<br \/>\n<\/span><span style=\"color: #000000;\">x = 1300 &#8211; 2y<br \/>\nThe solution table is<br \/>\n<\/span><\/span><\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">y<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">500<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">600<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">300<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">x<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">300<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">100<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">700<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-family: Georgia, Palatino;\"><span style=\"color: #000000; text-align: justify;\">For, x + 3y = 1300<br \/>\n<\/span><span style=\"color: #000000;\">x = 1300 &#8211; 3y<br \/>\n<\/span><span style=\"color: #000000;\">The solution table is<br \/>\n<\/span><\/span><\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">y<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">300<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">400<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">200<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">x<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">400<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">100<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">700<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">The graphical representation is as follows.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6171\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que2.png\" alt=\"NCERT Class 10 Maths Solution\" width=\"972\" height=\"739\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que2.png 972w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que2-300x228.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que2-768x584.png 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que2-850x646.png 850w\" sizes=\"auto, (max-width: 972px) 100vw, 972px\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: Georgia, Palatino;\"><span style=\"color: #000000;\"><strong>3. The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs.160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs.300. Represent the situation algebraically and geometrically.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>Solutions &#8211; <\/strong>Let the cost of 1 kg of apples be Rs. \u2018x\u2019<br \/>\n<\/span><span style=\"color: #000000;\">And, cost of 1 kg of grapes be Rs. \u2018y\u2019<br \/>\n<\/span><span style=\"color: #000000;\">According to the question, the algebraic representation is<br \/>\n<\/span><span style=\"color: #000000;\">2x + y = 160\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;&#8212;- (i)<br \/>\n<\/span><span style=\"color: #000000;\">4x + 2y = 300\u00a0 \u00a0 \u00a0 \u00a0 &#8212;&#8212;&#8212;&#8212;- (ii)<br \/>\n<\/span><span style=\"color: #000000;\">For, 2x + y = 160<br \/>\ny = 160 \u2212 2x<br \/>\nthe solution table is;<br \/>\n<\/span><\/span><\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">y<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">60<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">40<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">20<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">x<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">50<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">60<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">70<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">For 4x + 2y = 300<br \/>\ny = (300 &#8211; 4x)\/2,<br \/>\ny = 150 &#8211; 2x<br \/>\nthe solution table is;<br \/>\n<\/span><\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">y<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">10<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">-10<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">x<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">70<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">80<\/span><\/td>\n<td style=\"width: 25%;\"><span style=\"font-family: Georgia, Palatino;\">75<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">The graphical representation is as follows;<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6172\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que3.png\" alt=\"NCERT Class 10 Maths Solution\" width=\"676\" height=\"689\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que3.png 676w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que3-294x300.png 294w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/06\/NCERT-Class-10-Maths-Ex3.1-Que3-300x306.png 300w\" sizes=\"auto, (max-width: 676px) 100vw, 676px\" \/><br \/>\n<\/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<p>&nbsp;<\/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 3.1 has been provided here to help the students in solving the questions from this exercise. 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":[1045,1058,1059,1044,1049,1048],"class_list":["post-6018","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-3-1-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 3.1 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 10 Maths\u00a0Chapter - 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