Question

find the value of k for which the pair of linear equation kx+y=k² and x+my=1have infinitely many solutions

Answer 1

as pair of linear equations have infinitely many solutions , hence both lines coincide , that is 

k/1 =1/m =k^2 /1

hence k = k^2

so k^2 - k = 0
k(k -1 ) =0
so k=0 or k=1

Answer 2

Kx+y=K^2
x+my=1

Here,

Since, we know that an equation has to satisfy the following to get infinity solutions:-

a1/a2 = b1/b2 = c1/c2

So,

K/1 = 1/m = K^2/1

K/1 = K^2/1
K = K^2
0 = K^2-K
0 = K(K-1)
0 = K-1
K=1

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