Do you know that you can check your answers?
2x-2y+z=0
-2x+y+z=0
x=-3/4t, y=t,z=1/2t
Let's see...
-2x+y+z=0 ==> -2(-(3/4)t)+(t)+((1/2)t) = (3/2)t + t + (1/2)t = 3t
Hmmm...That doesn't look much like zero (0).
How did you find your answers? Solve each equation for 'y' and see what you get. Personally, I would have used 'z', but 'y' is fine.