Remember, the graph of a line represents every point that is a possible solution for the equation of that line. So when the graphs of two equations cross, the point of intersection lies on both lines, meaning that it is a possible solution for both equations. When the graphs of two equations never touch, there are no shared points and there are no possible solutions for the system. When the graphs of two equations lie on top of one another, they share all their points and every one is a possible solution.
