How do you solve the system of equations ##x+y=8##, ##x-y=4## by graphing?

Systems of equations can be solved by plotting each of them as a graph in one frame of axis. The intersection point(s) will be the solution(s) to the equation. If there are no intersection points, the system of equations doesn't have solutions.

In this system of equations you've got two linear equations, each of which can be represented as a line on the graph. The lines are not parallel, so there will be one solution in this case, which is the intersection point of two graphs.

Let's transform the equations into functions so that we can easily plot them. (1) ##y=-x+8## (2) ##y=x-4## You draw the graphs and find out that their intersection point is ##(6;2)##, that is ##x=6##, ##y=2##. This is the answer to the system of equations.