2x -  y = 3
4x + ky = 5

Solve by substitution, solve the first for y

2x - y = 3
    -y = 3 - 2x
     y = -3 + 2x

Substitute in the second equation:

4x + k(-3 + 2x) = 5
4x - 3k + 2kx = 5
4x + 2kx = 5 + 3k
 x(4 + 2k) = 5 + 3k

         x = 

This cannot be a solution if the denominator = 0,
so we set the denominator = 0

          4+2k = 0
            2k = -4
             k = -2

So if k = -2, there is no solution.

Edwin