NCERT Solutions for Class 9 Maths<\/a> Chapter 4 Linear Equations in Two Variables Ex 4.2 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\nNCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Exercise 4.2<\/h2>\n Question 1. \nWhich one of the following statements is true and why? \ny = 3x + 5 has \n(i) a unique solution. \n(ii) only two solutions. \n(iii) infinitely many solutions. \nSolution: \nWe have given the equation \ny = 3x + 5 \nPut x = 0, then y = 5 \nTherefore, (0, 5) is the solution of this equation. Again, put x = 1 then y = 8. \nTherefore, (1, 8) is also the solution to this equation. Again, put x = 2, then y = 11. \nTherefore, (2, 11) is also the solution of this equation. Again x = 3, x = 4 and so on. \nNow, it is clear that this equation has infinitely many solutions. \nNote: A linear equation in two variables has infinitely many solutions.<\/p>\n
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Question 2. \nWrite four solutions for each of the following equations. \n(i) 2x + y = 7 \n(ii) \u03c0x + y = 9 \n(iii) x = 4y \nSolution: \n(i) We have 2x + y = 7 \nPut x = 0 then y = 7 \nTherefore, (0, 7) is the solution of this equation. \nAgain put x = 1, then y = 5. \nTherefore (1, 5) is also the solution of this equation. Again put x = 2, then y = 3. \nTherefore (2, 3) is also the solution of this equation. Again put x = 3 then y = 1. \nTherefore (3, 1) is also the solution of this equation. \nTherefore, (0, 7), (1, 5), (2, 3) and (3, 1) are the four solutions of the equation 2x + y = 7.<\/p>\n
(ii) We have given \u03c0x + y = 9 \nor, \\(\\frac {22}{7}\\) x + y = 9 (\u2235 \u03c0 = \\(\\frac {22}{7}\\)) \nor, y = 9 – \\(\\frac {22}{7}\\) x \nPut x = 0 then y = 9 \nTherefore (0, 9) is the solution of this equation. \nAgain, put x = 1 then y = \\(\\frac {41}{7}\\) \nTherefore (\\(\\frac {22}{7}\\)) is also the solution of this equation. \nAgain put x = 7, then y = -13 \nTherefore (7, – 13) is also the solution of this equation. \nAgain put x = 14, then y = -3 \nTherefore (14, -35) is also the solution of this equation. \nHence (0, 9) (\\(\\frac {22}{7}\\)) (7, 13) and (14, -35) are the four solutions of equation \u03c0x + y = 9<\/p>\n
(iii) We have given that x = 4y \nPut y = 0, then x = 0 \nTherefore, (0, 0) is the solution of this equation. \nAgain put y = 1, then x = 4 Therefore, (4, 1) is also the solution of this equation. \nAgain, put y = 2 then x = 8 Therefore, (8, 2) is also the solution of this equation. \nAgain put y = 3, then x = 12 Therefore, (12, 3) is also the solution of this equation. \nHence, (0, 0), (4, 1) (8, 2), and (12, 3) are the four solution of equation x = 4y.<\/p>\n
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Question 3. \nCheck which of the following are solutions of the equation x – 2y = 4 and which are not. \n(i) (0, 2) \n(ii) (2, 0) \n(iii) (4, 0) \n(iv) (\u221a2, 4\u221a2) \n(v) (1, 1) \nSolution: \n(i) we have given that x – 2y = 4 \nPut x = 0 and y = 2 \nThen, 0 – 2 \u00d7 2 = 4 \n-4 = 4 \nHere, L.H.S. \u2260 R.H.S. \nTherefore, (0, 2) is not the solution of equation x – 2y = 4<\/p>\n
(ii) Put x = 2 and y = 0 \nThen, 2 – 2 \u00d7 0 = 4 \n2 = 4 \nHere, L.H.S. \u2260 R.H.S. \nTherefore (2, 0) is not the solution of equation x – 2y = 4<\/p>\n
(iii) Put x = 4 and y = 0 in equation x – 2y = 4 \nThen 4 – 2 \u00d7 0 = 4 \n4 = 4 \nHere, L.H.S. = R.H.S. \nTherefore, (4, 0) is the solution of equation x – 2y = 4<\/p>\n
(iv) Put x = \u221a2 and y = 4\u221a2 in equation x – 2y = 4 \nThen \u221a2 – 2 \u00d7 4\u221a2 = 4 \n\u221a2 – 8\u221a2 = 4 \n-7\u221a2 = 4 \nHere, L.H.S. \u2260 R.H.S. \nTherefore, (\u221a2, 4\u221a2) is not the solution of equation x – 2y = 4.<\/p>\n
(v) (1, 1) \nPut x = 1 and y = 1 in equation x – 2y = 4 \nThen 1 – 2 \u00d7 1 = 4 \n1 – 2 = 4 \n-1 = 4 \nL.H.S. \u2260 R.H.S. \nTherefore (1, 1) is not the solution of equation x – 2y = 4.<\/p>\n
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Question 4. \nFind the value of k if x = 2, y = 1 is a solution of the equation 2x + 3y = k. \nSolution: \nWe have given that x = 2 and y = 1 is the solution of the equation 2x + 3y = k. \nPut x = 2 and y = 1 in equation 2x + 3y = k \n2 \u00d7 2 + 3 \u00d7 1 = k \n4 + 3 = k \nk = 7 \nHence, the value of k in equation 2x + 3y = k is 7.<\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.2 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Exercise 4.2 Question 1. Which one of the following statements is true and why? y …<\/p>\n
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.2<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[6],"tags":[],"yoast_head":"\nNCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.2 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n