The general form of a system in three variables x,y,z has equation in the general form:

akx+bky+ckz=dk

If one of the coefficients ck of the variables z is zero, we can isolate y and bring that equation to the form y=mx+b.

akx+bky=dk

bky=-akx+dk

\(y=-(\frac{ak}{bk})x+\frac{dk}{bk}\)