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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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