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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.