Suppose you are asked to solve the simultaneous equations \begin{cases}x-y=2 \\2 x+3 y=10\end{cases}. In fact, each equation represents a line, if drawn on a 2-D coordinate plane.

Thus, solving the simultaneous equations is similar to finding the intersection point of two lines.

Consider solving two simultaneous equations for two unknowns. Interpreting geometrically, we want to find the intersection point(s) of two lines. There are three possible scenarios: