On a graph, the solution to a system of linear equations is represented by

the x–intercept of each line
the y–intercept of each line
all the points on either line
the intersection of the lines

If you have a system of 2 linear equations you can draw them on a graph. Once you do that you will see that (if you scale graph properly) every 2 lines (if they are not parallel to each other! ) have one point at which they cross each other. Coordinates of that point belong to both first and second linear equation and therefore it is the solution to that system. If you pick any other point on first or second line it will belong to one but not to other line!

The solution has to be a dot that belongs to both lines.

Answer is: The intersection of the lines.