Question

Find the values of k for which the pair of linear equations kx+y=k^2 and x+ky=1 have infinitely many solutions

Answer 1

kx+y=k^2
x+ky=1

For a system of linear equation to have infinite solutions
a1/a2=b1/b2=c1/c2

a1=k
a2=1

b1=1
b2=k

c1=k^2
c2=1

So,
k=1/k
k^2=1
k=+-1

Also
k=k^2
k+=1

From above k=1

Answer 2

For solution refer to the attached picture.Hope it helps!