If the graphs of the equations in a system of linear equations coincide with each other, what does that tell you about the solution of the system?

 If by "coincide", in other words this is also known as intersect, it means that the solution to the system is that intersection point. For instance, if the intersection point of the 2 lines is (5,7) on the graph, it means that in both equations, x = 5 and y = 7. If you mean that the 2 equations result in the same line, it means that the 2 equations were really equal, but that one could be basic to be identical with the other. For example, if you have 2x + 2y = 8 and 4x + 4y = 16, they will give you the same line, and you can see that if you divide that second equation by 2 all the way crossways, it merely shows the first equation.