Question

hwat is the value of k if the system has no solution:
2x-y=3
4x+ky=4

Answer 1

2x = 3 + y

2(3+y) + ky = 4
6 + 2y + ky = 4
y(2+k) = -2
y = -2 / (2+k)

k = -2

Answer 2

coolsector has a good answer, but you can do it with your eyeball. 4x is twice 2x so make sure that ky is twice -y i.e. k = -2