When working with two equations (aka a system of equations), the solution is (or the solutions are) where the graphs intersect.
If they intersect once, there's one solution.
If they intersect twice, there are two solutions.
The solution IS the point(s) of intersection.
Every point on a line is also a solution to the equation that makes the line. Since that interseciton point is on both lines, it's a solution for both lines.
