Plot the two linear equations on the same graph. First, x+y=4, that is, y=4-x; the intercepts are y intercept=4 and x intercept=4. The straight line passing through 4 on the y axis and 4 on the x axis is the graph of x+y=4.
The x and y intercepts for x-y=2 (or y=x-2) are x=2 and y=-2. Mark these points on the axes and draw a line through them, intersecting the other straight line graph. The lines cross (at right angles) at one point which is the solution of the system of equations. Add the two equations: 2x=6, making x=3; substitute 3 for x in either equation: 3+y=4 or 3-y=2, so y=1.
The point of intersection is (3,1) and the solution of the system of equations is x=3 and y=1; these are equivalent statements.