{"id":4918,"date":"2026-06-20T12:46:56","date_gmt":"2026-06-20T07:16:56","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=4918"},"modified":"2026-06-21T11:31:22","modified_gmt":"2026-06-21T06:01:22","slug":"ncert-class-10-maths-chapter-3-exercise-3-1-solutions-pair-of-linear-equations","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-10-maths-chapter-3-exercise-3-1-solutions-pair-of-linear-equations\/","title":{"rendered":"NCERT Class 10 Maths Chapter 3 Exercise 3.1 Solutions | Pair of Linear Equations"},"content":{"rendered":"<div class=\"mymoc-top mymoc-entity-placement\" id=\"mymoc-4199142011\"><div id=\"mymoc-2344728958\"><a href=\"https:\/\/amzn.to\/4ehRB6n\" aria-label=\"printers\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers-300x73.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers-1024x250.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers-768x187.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"318\"><\/a><\/div><\/div><div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/4918?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">4<\/span><\/div>\n<h1 class=\"wp-block-heading\">Short Introduction<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we provide complete and detailed solutions of <strong>NCERT Class 10 Maths Chapter 3 &ndash; Pair of Linear Equations in Two Variables, Exercise 3.1<\/strong>. The exercise is based on the graphical representation of linear equations and the conditions for consistent and inconsistent pairs of equations. All questions are solved step by step in simple language for CBSE and State Board students.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Particular<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Class<\/td><td>10<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Chapter<\/td><td>3<\/td><\/tr><tr><td>Chapter Name<\/td><td>Pair of Linear Equations in Two Variables<\/td><\/tr><tr><td>Exercise<\/td><td>3.1<\/td><\/tr><tr><td>Method Used<\/td><td>Graphical Method<\/td><\/tr><tr><td>Board<\/td><td>CBSE &amp; State Boards<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Easy to Moderate<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Pair of linear equations in two variables<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Graphical solution of linear equations<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Consistent and inconsistent equations<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Intersecting, parallel and coincident lines<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10004; Comparing ratios:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a&#8321;\/a&#8322;<\/li>\n\n\n\n<li>b&#8321;\/b&#8322;<\/li>\n\n\n\n<li>c&#8321;\/c&#8322;<\/li>\n<\/ul>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/ncert-class-10-maths-real-number-exercise-1-2-solutions-mymockmate\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 10 Maths Real Number Exercise 1.2 Solutions |  MyMockMate<\/span><\/a><\/div><p class=\"wp-block-paragraph\">&#10004; Formation of linear equations from word problems.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">General Form of Linear Equation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">ax + by + c = 0<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conditions of Solutions<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Unique Solution (Intersecting Lines)<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">a&#8321;\/a&#8322; &ne; b&#8321;\/b&#8322;<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>No Solution (Parallel Lines)<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">a&#8321;\/a&#8322; = b&#8321;\/b&#8322; &ne; c&#8321;\/c&#8322;<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>Infinitely Many Solutions (Coincident Lines)<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">a&#8321;\/a&#8322; = b&#8321;\/b&#8322; = c&#8321;\/c&#8322;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 1 Form the pair of linear equations in the following problems, and find their solutions<br>graphically.<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>(i) 10 students of Class X took part in a Mathematics quiz. The number of girls is 4 more than the number of boys. Find the number of boys and girls.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-167-859x1024.png\" alt=\"\" class=\"wp-image-4921\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-167-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-167-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-167-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-167.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 1 (ii)<\/h1>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-10-maths-exercise-2-1-solutions-polynomials-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 10 Maths Exercise 2.1 Solutions | Polynomials<\/span><\/a><\/div><p class=\"wp-block-paragraph\"><strong>5 pencils and 7 pens together cost <code>50, whereas 7 pencils and 5 pens together cost<\/code> 46. Find the cost of one pencil and that of one pen.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-171-1024x683.png\" alt=\"\" class=\"wp-image-4931\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-171-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-171-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-171-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-171-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-171.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>On comparing the ratios a<sub>1<\/sub>\/a<sub>2<\/sub>,  b<sub>1<\/sub>\/b<sub>2<\/sub> and c<sub>1<\/sub>\/c<sub>2<\/sub> , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">5x&minus;4y+8=0<\/p><div class=\"mymoc-middle mymoc-entity-placement\" id=\"mymoc-399296568\"><div id=\"mymoc-393928201\"><a href=\"https:\/\/amzn.to\/43YYZi3\" aria-label=\"smart-phones\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-300x76.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-1024x259.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smart-phones-768x194.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"329\"><\/a><\/div><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">7x+6y&minus;9=0<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-170-1024x683.png\" alt=\"\" class=\"wp-image-4929\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-170-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-170-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-170-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-170-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-170.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(ii)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">9x+3y+12=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">18x+6y+24=0<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"611\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-172-1024x611.png\" alt=\"\" class=\"wp-image-4934\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-172-1024x611.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-172-300x179.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-172-768x458.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-172-1536x916.png 1536w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-172.png 1624w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iii)<\/h2>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-10-maths-exercise-2-2-solutions-relationship-between-zeroes-and-coefficients\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">Class 10 Maths Exercise 2.2 Solutions | Relationship Between Zeroes and Coefficients<\/span><\/a><\/div><p class=\"wp-block-paragraph\">6x&minus;3y+10=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2x&minus;y+9=0<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-173-1024x683.png\" alt=\"\" class=\"wp-image-4936\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-173-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-173-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-173-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-173-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-173.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>On comparing the ratios a<sub>1<\/sub>\/a<sub>2<\/sub>,  b<sub>1<\/sub>\/b<sub>2<\/sub> and c<sub>1<\/sub>\/c<sub>2<\/sub> , find out whether the lines representing the following pairs of linear equations intersect at a point, are coincident or inconsistent.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">3x+2y=5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2x&minus;3y=7<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-179-1024x576.png\" alt=\"\" class=\"wp-image-4954\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-179-1024x576.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-179-300x169.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-179-768x432.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-179-1536x864.png 1536w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-179.png 1672w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(ii)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">2x&minus;3y=8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">4x&minus;6y=9<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-181-1024x683.png\" alt=\"\" class=\"wp-image-4958\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-181-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-181-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-181-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-181-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-181.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iii)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">3x\/2 +5y\/3 =7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">9x&minus;10y=14<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-180-1024x683.png\" alt=\"\" class=\"wp-image-4957\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-180-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-180-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-180-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-180-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-180.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iv)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">5x&minus;3y=11<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&minus;10x+6y=&minus;22<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-182-1024x683.png\" alt=\"\" class=\"wp-image-4961\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-182-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-182-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-182-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-182-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-182.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(v)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">(4x\/3)+2y=8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2x+3y=12<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-183-1024x683.png\" alt=\"\" class=\"wp-image-4964\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-183-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-183-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-183-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-183-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-183.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 4 <\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Which of the following pairs of linear equations are consistent\/inconsistent? If consistent, obtain the solution graphically:<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">x+y=5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2x+2y=10<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-184-1024x683.png\" alt=\"\" class=\"wp-image-4966\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-184-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-184-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-184-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-184-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-184.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">(ii)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">x&minus;y=8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3x&minus;3y=16<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-185-1024x683.png\" alt=\"\" class=\"wp-image-4969\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-185-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-185-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-185-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-185-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-185.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iii)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">2x+y&minus;6=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">4x&minus;2y&minus;4=0<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-186-1024x683.png\" alt=\"\" class=\"wp-image-4972\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-186-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-186-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-186-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-186-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-186.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iv)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">2x&minus;2y&minus;2=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">4x&minus;4y&minus;5=0<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-187-1024x683.png\" alt=\"\" class=\"wp-image-4974\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-187-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-187-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-187-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-187-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-187.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 5<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-190-683x1024.png\" alt=\"\" class=\"wp-image-4985\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-190-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-190-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-190-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-190-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-190.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 6<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Given the linear equation 2x + 3y &ndash; 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:<br>(i) intersecting lines.             (ii) parallel lines          (iii) coincident lines<\/strong><br><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-189-683x1024.png\" alt=\"\" class=\"wp-image-4983\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-189-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-189-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-189-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-189-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-189.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 7<\/h1>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Draw the graphs of the equations x &ndash; y + 1 = 0 and 3x + 2y &ndash; 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-188-683x1024.png\" alt=\"\" class=\"wp-image-4979\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-188-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-188-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-188-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-188-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-188.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Comparing ratios incorrectly.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Using wrong sign of c.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Confusing parallel and coincident lines.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#10060; Making mistakes while forming equations from word problems.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Learn all three conditions of ratios.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Practice graph plotting.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Draw proper tables while solving graphically.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Write final answers with units.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">1. If a&#8321;\/a&#8322; &ne; b&#8321;\/b&#8322;, then the equations have:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. No solution<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Infinite solutions<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Unique solution<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. None<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> C<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">2. Coincident lines have:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. One solution<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Infinite solutions<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. No solution<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Two solutions<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">3. Parallel lines are:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. Consistent<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Inconsistent<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Dependent<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. None<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">4. Intersecting lines are:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. Consistent<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Inconsistent<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Dependent<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. None<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer:<\/strong> A<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Frequently Asked Questions (FAQs)<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Q1. What is a pair of linear equations?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Two linear equations containing the same variables are called a pair of linear equations.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q2. When do equations have infinitely many solutions?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">When<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a&#8321;\/a&#8322; = b&#8321;\/b&#8322; = c&#8321;\/c&#8322;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q3. What are inconsistent equations?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Equations having no common solution.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Q4. Which method is used in Exercise 3.1?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Mainly graphical method and comparison of ratios.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<p class=\"wp-block-paragraph\">&#128218; For more NCERT Solutions, Important Questions, Notes, Mock Tests and Board Exam Preparation Materials, visit:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#127760; <strong><a href=\"http:\/\/www.mymockmate.com\/\">www.mymockmate.com<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#128640; Practice smarter and score higher with MyMockMate!<\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/4918?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">4<\/span><\/div>\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n<div class=\"mymoc-bottom mymoc-entity-placement\" id=\"mymoc-3920424451\"><div id=\"mymoc-2709601082\"><a href=\"https:\/\/amzn.to\/440rYSB\" aria-label=\"ssd\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/ssd.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/ssd.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/ssd-300x50.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/ssd-1024x171.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/ssd-768x128.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"218\"><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p> 4 Short Introduction In this article, we provide complete and detailed solutions of NCERT Class 10 Maths<\/p>\n","protected":false},"author":1,"featured_media":4919,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[5,10],"tags":[48,3512,3513,3515,3514,3516,3510,639,3511],"class_list":["post-4918","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-10","category-maths-class-10","tag-cbse-class-10-maths","tag-chapter-3-maths-solutions","tag-class-10-maths-chapter-3","tag-exercise-3-1-answers","tag-graphical-method","tag-maths-chapter-3-solutions","tag-ncert-class-10-maths-exercise-3-1-solutions","tag-ncert-solutions-class-10","tag-pair-of-linear-equations-in-two-variables"],"featured_image_src":"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/NCERT-Class-10-Maths-Chapter-3-Exercise-3.1-Solutions-Pair-of-Linear-Equations.png","author_info":{"display_name":"Team Mymockmate","author_link":"https:\/\/mymockmate.com\/notes\/author\/bsm_adm\/"},"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/4918","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=4918"}],"version-history":[{"count":20,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/4918\/revisions"}],"predecessor-version":[{"id":4986,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/4918\/revisions\/4986"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/4919"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=4918"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=4918"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=4918"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}