{"id":24950,"date":"2021-06-21T16:46:50","date_gmt":"2021-06-21T11:16:50","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=24950"},"modified":"2022-03-02T10:38:06","modified_gmt":"2022-03-02T05:08:06","slug":"ncert-solutions-for-class-9-maths-chapter-4-ex-4-2","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-4-ex-4-2\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.2"},"content":{"rendered":"

These 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>\n

NCERT 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

\"NCERT<\/p>\n

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

\"NCERT<\/p>\n

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

\"NCERT<\/p>\n

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<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-4-ex-4-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.2 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"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. 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