Question

find values ok k for which linear pair equation kx+y=k^2 and x+ky=1 have infinity many solutions

Answer 1

for infinite many solution,
we have
a1/a2=b1/b2=c1/c2
now on taking
a1 /a2=b1/b2
k/1=1/k
k^2=1
k=1.
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Answer 2

k=-1 , 1 ,0 , (-1+√3i)/2 , (-1-√3i)/2