Question

find the values of k for which the pair of linear equations kx+y=x*and x+ky=1 have infinity many solutions

Answer 1

it doesn't have infinitely many solutions
the question would be 
Find the value(s) of k for which the pair of linear equations kx + y = k2 and x + ky = 1 have infinitely many solutions.

please recheck

Answer
For pair of equations kx + 1y = k2 and 1x + ky = 1
We have:
a1/a2 = k/1
b1/b2 = 1/k
c1/c2 = k2/1
For infinitely many solutions,
a1/a2 = b1/b2 = c1/c2
k/1 = 1/k
k2 = 1
k = 1, -1 ... (i)
1/k = k2/1
k3 = 1
k = 1 ... (ii)
From (i) and (ii),
k = 1