Find the value(s) of k for which the pair of linear equations k x + y = k 2 and x + k y = 1 have infinitely many solutions.

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

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Find values of k for which kx + y = k^2 and x + ky = 1 have infinitely

Question 9 - CBSE Class 10 Sample Paper for 2018 Boards - Part 2
Question 9 - CBSE Class 10 Sample Paper for 2018 Boards - Part 3

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Transcript

Question 9 Find the value(s) of k for which the pair of linear equations kx + y = k2 and x + ky = 1 have infinitely many solutions. kx + y = k2 i.e. kx + y k2 = 0 x + ky = 1 i.e. x + ky 1 = 0 kx + y k2 = 0 Comparing with a1x + b1y + c1 = 0 a1 = k , b1 = 1 , c1 = k2 x + ky 1 = 0 Comparing with a2x + b2y + c2 = 0 a2 = 1 , b2 = k , c2 = 1 Since equation has infinite number of solutions So, 1/ 2 = 1/ 2 = 1/ 2 Putting in values /1 = 1/ = ( ^2)/( 1) /1 = 1/ = ^2/1 Solving / = / k2 =1 k = 1 k = 1 So, k = 1, 1 Solving / = ^ / 1 = k3 k3 = 1 k3 = 13 k = 1 Therefore, k = 1 satisfies both equations. Hence k = 1 is the answer

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.