Look, ordered pairs are points in the plane. Lines are collections of points in the plane. These points, (p,q), satisfy the equations of lines, ax+by=c, that is a*p+b*q=c. All I have to do is find two points (u,v) & (t,s) such that a*u+b*x=c & a*t+b*s=c. Two points determine a line! The way we find these points is not fixed. So you may solve for one of the variables, either x or y. But, this is not necessary! To graph a line, all we need is two points.
PKA