Question

For what value of k will the following pair of linear equations have infinite number of solutions
kx + 4y = k- 4
16x + ky = k

Answer 1

For pair of linear equations have infinite number of solutions, it should satisfy

a1/a2 = b1/b2 = c1/c2

Given equations are:
kx + 4y = k- 4
16x + ky = k

Thus, k/16 = 4/k = (k-4)/k

Using first part of equation:
k/16 = 4/k

Or k^2 = 16×4 = 64

Or k =√64 = 8 or -8

Using second part of equation:
4/k = (k-4)/k

Or 4 = k-4

Or k = 4+4 = 8

We can see that k =8 satisfies all.

So value of k is 8.