x + ky=1

kx - 3ky = 2k+3

We can assume that k is a parameter, now you solve it becomes a two equitation with two variables x and y.

Now we solve it,

multiply the first equation by 3 and add to the second one.

You get:

3x + 3ky +kx-3ky=3+2k+3

3x +kx=6+2k

x(3+k)=2(3+k)

x=3

I let you find y...