{"id":34582,"date":"2018-12-26T08:34:56","date_gmt":"2018-12-26T08:34:56","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=34582"},"modified":"2020-11-27T13:39:49","modified_gmt":"2020-11-27T08:09:49","slug":"ncert-solutions-for-class-10-maths-chapter-3-ex-3-5","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths-chapter-3-ex-3-5\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5"},"content":{"rendered":"<p>NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 are part of <a class=\"button-red\" href=\"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths\/\">NCERT Solutions for Class 10 Maths<\/a>. Here are we have given Chapter 3 <strong>Pair of Linear Equations in Two Variables\u00a0Class 10 NCERT Solutions Ex 3.5.\u00a0<\/strong><\/p>\n<ul>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1\" href=\"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths-chapter-3\/\" target=\"_blank\" rel=\"noopener\">Pair of Linear Equations in Two Variables Class 10 Ex 3.1<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2\" href=\"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths-chapter-3-ex-3-2\/\" target=\"_blank\" rel=\"noopener\">Pair of Linear Equations in Two Variables Class 10 Ex 3.2<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3\" href=\"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths-chapter-3-ex-3-3\/\" target=\"_blank\" rel=\"noopener\">Pair of Linear Equations in Two Variables Class 10 Ex 3.3<\/a><\/li>\n<li><a title=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4\" href=\"https:\/\/www.aplustopper.com\/ncert-solutions-for-class-10-maths-chapter-3-ex-3-4\/\" target=\"_blank\" rel=\"noopener\">Pair of Linear Equations in Two Variables Class 10 Ex 3.4<\/a><\/li>\n<\/ul>\n<table style=\"table-layout: fixed; width: 650px;\" border=\"1\">\n<tbody>\n<tr>\n<td><strong>Board<\/strong><\/td>\n<td>CBSE<\/td>\n<\/tr>\n<tr>\n<td><strong>Textbook<\/strong><\/td>\n<td>NCERT<\/td>\n<\/tr>\n<tr>\n<td><strong>Class<\/strong><\/td>\n<td>Class 10<\/td>\n<\/tr>\n<tr>\n<td><strong>Subject<\/strong><\/td>\n<td>Maths<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter<\/strong><\/td>\n<td>Chapter 3<\/td>\n<\/tr>\n<tr>\n<td><strong>Chapter Name<\/strong><\/td>\n<td>Pair of Linear Equations in Two Variables<\/td>\n<\/tr>\n<tr>\n<td><strong>Exercise<\/strong><\/td>\n<td>Ex 3.5<\/td>\n<\/tr>\n<tr>\n<td><strong>Number of Questions Solved<\/strong><\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td><strong>Category<\/strong><\/td>\n<td>NCERT Solutions<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5<\/h2>\n<p>Page No: 62<\/p>\n<p><strong>Question 1.<\/strong> Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.<br \/>\n(i) <i>x<\/i> \u2013 3<i>y<\/i> \u2013 3 = 0 ; 3<i>x<\/i> \u2013 9<i>y<\/i> \u2013 2 =0<br \/>\n(ii) 2<i>x<\/i> + <i>y<\/i> = 5 ; 3<i>x<\/i> +2<i>y<\/i> =8<br \/>\n(iii) 3<i>x<\/i> \u2013 5<i>y<\/i> = 20 ; 6<i>x<\/i> \u2013 10<i>y<\/i> =40<br \/>\n(iv) <i>x<\/i> \u2013 3<i>y<\/i> \u2013 7 = 0 ; 3<i>x<\/i> \u2013 3<i>y<\/i> \u2013 15= 0<\/p>\n<div>\n<p><strong>Solution:<br \/>\n<\/strong><\/p>\n<div class=\"solnBox\">\n<div class=\"table-responsive\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100209\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-61.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 61\" width=\"307\" height=\"193\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-61.jpg 307w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-61-300x189.jpg 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nThus, the given pair of equations has no solution.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100210\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-62.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 62\" width=\"245\" height=\"193\" \/><br \/>\nThus, the given pair of equations has unique solution.<br \/>\nBy cross-multiplication method,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100212\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-63.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 63\" width=\"206\" height=\"168\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100213\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-64.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 64\" width=\"350\" height=\"193\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-64.jpg 350w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-64-300x165.jpg 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><br \/>\nThus, the given pair of equations has infinite solutions.<br \/>\nThe solutions can be obtained by assuming the value of\u00a0<em>x<\/em>\u00a0to be\u00a0<em>k<\/em>, where\u00a0<em>k<\/em>\u00a0is any<br \/>\nconstant. So, the ordered pairs <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100214\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-65.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 65\" width=\"93\" height=\"47\" \/>, where\u00a0<em>k<\/em>\u00a0is a constant, are the solutions of<br \/>\nthe given pair of equations.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100215\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-66.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 66\" width=\"313\" height=\"193\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-66.jpg 313w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-66-300x185.jpg 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><br \/>\nThus, the given pair of equations has unique solution.<br \/>\nBy cross-multiplication,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100216\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-67.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 67\" width=\"206\" height=\"129\" \/><\/p>\n<p>Concept Insight: In order to answer such questions, remember the condition for the pair of linear equations to have unique, infinitely many or no solution relating the coefficients. Also, remember the formula used to solve by cross multiplication method. While applying the formula, be careful about the signs of the coefficients. And above all don&#8217;t forget to first write the linear equations in standard form which is ax + by + c = 0.<\/p>\n<\/div>\n<\/div>\n<p><strong>Question 2.<\/strong><br \/>\n(i) For which values of a and b does the following pair of linear equations have an infinite number of solutions?<br \/>\n2<i>x<\/i> + 3<i>y<\/i> =7<br \/>\n(<i>a<\/i> \u2013 <i>b<\/i>)<i>x<\/i> + (<i>a<\/i> + <i>b<\/i>)<i>y<\/i> = 3<i>a<\/i> +<i>b<\/i> \u20132<\/p>\n<\/div>\n<div><strong>Solution:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100217\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-68.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 68\" width=\"651\" height=\"534\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-68.png 651w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-68-300x246.png 300w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><br \/>\n<\/strong><\/div>\n<p>(ii) For which value of k will the following pair of linear equations have no solution?<br \/>\n3<i>x<\/i> + <i>y <\/i>= 1<br \/>\n(2<i>k<\/i> \u20131)<i>x<\/i> + (<i>k<\/i> \u20131)<i>y<\/i> = 2<i>k<\/i> + 1<\/p>\n<div>\n<p><strong>Solution:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100218\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-69.png\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 69\" width=\"580\" height=\"371\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-69.png 580w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-69-300x192.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><br \/>\n<\/strong><\/p>\n<p>Concept Insight:\u00a0In order to solve such problems, firstly write the linear equations in standard form which is ax + by + c = 0.To find the value of the unknowns, the key idea is to remember the conditions for a given pair of equations to have infinite solutions and no solution.\u00a0 In case of infinite solutions rule out the values which does not satisfy all the ratios. Also, be careful about the signs of the coefficients.<\/p>\n<\/div>\n<p><strong>Question 3.<\/strong> Solve the following pair of linear equations by the substitution and cross-multiplication methods:<br \/>\n8<i>x<\/i> +5<i>y<\/i> = 9<br \/>\n3<i>x<\/i> +2<i>y<\/i> = 4<\/p>\n<p><strong>Solution:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100219\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-70.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 70\" width=\"177\" height=\"107\" \/><br \/>\n<\/strong>Substituting this value of y in equation (1), we obtain:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100220\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-71.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 71\" width=\"259\" height=\"90\" \/><br \/>\n\u2234 x = -2, y = 5<br \/>\nCross-multiplication method:<strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100221\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-72.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 72\" width=\"239\" height=\"254\" \/><br \/>\n<\/strong><\/p>\n<p>Concept Insight:\u00a0In order to solve the given pair of equations by cross multiplication method, remember the formula to be used and convert the system of equations to standard form. While applying the formula, be careful about the signs of the coefficients.\u00a0In order to solve the given pair of equations by substitution method, substitute the value of any one of the variable from any one of the equation. Make sure you substitute the value of that variable which simplifies your calculations.<br \/>\nSolution will be same in both cases.<\/p>\n<p><strong>Question 4.<\/strong> Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:<\/p>\n<p>(i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.<\/p>\n<div><strong>Solution:<br \/>\n<\/strong>Let the fixed charge of the food and the charge for food per day be x and y respectively.<br \/>\nAccording to the question,<br \/>\nx + 20y = 1000\u00a0\u00a0\u00a0\u00a0 &#8230;(1)<br \/>\nx + 26y = 1180\u00a0\u00a0 &#8230;(2)<br \/>\nSubstituting this value of y in equation (1) from equation (2), we obtain<br \/>\n6y = 180<br \/>\ny = 30<br \/>\nSubstituting this value of y in equation (1), we obtain:<br \/>\nx+ 20 x 30 = 1000<br \/>\nx = 1000 &#8211; 600<br \/>\nx = 400<br \/>\nThus, the fixed charge of the food and the charge per day are Rs 400 and Rs 30 respectively.Concept Insight:\u00a0Here, the fixed charge of the food and charge for food per day are the unknown quantities. So they are taken as variables x and y. The two equations can then be obtained by using the given conditions. You will observe that the variable x has the same coefficient in both the equations, so it will be easier to find the solution by eliminating x from both the equations. Also, one can solve the system by other methods.<\/div>\n<div>(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.<\/div>\n<div><\/div>\n<div><strong>Solution:<br \/>\n<\/strong>Let the fraction be x\/y\u00a0According to the question,\u00a0<strong><br \/>\n<\/strong>According to the question,\u00a0<strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-100222\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/NCERT-Solutions-for-Class-10-Maths-Chapter-3-Pair-of-Linear-Equations-in-Two-Variables-73.jpg\" alt=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables 73\" width=\"184\" height=\"152\" \/><br \/>\n<\/strong>Subtracting equation (1) from equation (2), we obtain:<br \/>\nx = 5<br \/>\nPutting the value of x in equation (1), we obtain:<br \/>\n15 &#8211; y = 3<br \/>\ny = 12<br \/>\nThus the fraction is 5\/12.<\/div>\n<div>\n<p>Concept Insight:\u00a0Since the problem asks for a fraction. The numerator and denominator of the fraction need to be represented by variables. A pair of linear equations can be obtained from the given conditions. Observe that the variable y has the same coefficient in both the equations, so it will be easier to find the solution by eliminating y from both the equations.<\/p>\n<\/div>\n<p>We hope the NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 3 Pair of Linear Equations in Two Variables\u00a0Class 10 NCERT Solutions Ex 3.5.\u00a0 Pair of Linear Equations in Two Variables Class 10 Ex [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[6805],"tags":[36685],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 - A PlusTopper.com<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 helpful to finish your Home Work. 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