The solution to a system of (linear) equations is the point where the graphs intersect. Consider two parallel lines. By definition, two parallel lines never intersect each other, but all pairs of non-parallel lines will eventually intersect. That means they will also have a solution.
Let's consider what makes a line parallel to another line. It basically looks identical, having the same steepness (slope), but the graph is just shifted over. That is, a parallel line would have the same slope and a different y-intercept. For our equation [tex]2y-4x=12[/tex], or [tex]y=2x+6[/tex] in slope-intercept form, a parallel line will be of the form [tex]y=2x+b[/tex].
That describes the form of a parallel line, which we do not want. Any other line, however, will give a solution to our system, so we merely want a line where the slope does not equal 2.
We can have any equation of the form [tex]y=mx+b, \ x \neq 2[/tex].
