Here are my answers. Can you check if I got the right answers? Thank you!

Solve for z:

4x+10yx=0
z=-2x/5y

y^2+3yz-8z-4x=0
z=(-y^2+4x)/(3y-8)

there was no z in your first equation, from you answer I can tell it should have been 4x + 10yz = 0
If so, the answer is right.

last one is right