Question

Find the value of k for which pair of linear equation kx+y=k^2 and x+ky=1 for infinite solution

Answer 1

If the linear equations have infinite solutions then
$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$
Therefore
$\frac{k}{1} = \frac{1}{k} = \frac{ {k}^{2} }{1} \\ \\ {k}^{2} = {k}^{2} = 1 \\ {k}^{2} = 1 \\ k = 1$
Hence the value of K is 1.

Answer 2

kx/x=y/ky=k²/1
k=1
so now since it is infinitely many solutions k³=k
k²=1
k=1