Question

Find the value(s) of k for which the pair of linear equations kx + y = k2 and x + ky = 1have infinitely many solutions.

Answer 1

For a pair of linear equations to have infinite solutions ,

Ratio of Coefficients of x = Ratio of coefficients of y = Ratio of constants .

k/1 = 1/k = k² /1

k / 1 = k /1

k² = 1

k= ±1

Now.

1/k = k² /1

k³ = 1

k = 1 .

Therefore, For K = 1 ,The system of linear equations has infinite solutions