Question

find the value of k for which the pair of linear equation kx + Y=k^2 and X + ky= 1 have a infinitely many solution

Answer 1

value of k in this question is one.

Answer 2

Hi there!

Since,
The Eqn. have infinitely many solutions

$\frac{ {a}_{1} }{ {a}_{2} } \: = \: \frac{ {b}_{1} }{ {b}_{2} } \: = \: \frac{ {c}_{1} }{ {c}_{2} }$

Thus,
On Comparing the coefficients of x and y

$\frac{ k}{ 1} \: = \: \frac{ 1}{ k} \: = \: \frac{ 2k}{ 1}$

Therefore,

k = 1 or -1
k = 1/ √2 or -1/ √2

[ Thank you! for asking the question. ]
Hope it helps!