Before copying the answer of JoecelE, the equation he used is derived from the system, and you must show from where it come from. x + y = 23; x -y = 7. The second equation in terms of x is -y = -x + 7 or y = x - 7. Use x + 7 in the first equation instead of y. Therefore, x + y = 23 becomes x + (x - 7) = 23. Simplify 2x - 7 = 23; then, 2x - 7 + 7 = 23 + 7; 2x = 30; 2x/2 = 30/2. x = 15. There is only one solution: x = 15; y = 8. Therefore, the solution of the system is (x,y) = (15, 8)
I mean SHOULD derived from the system. So in terms of x using any of the equation, x = 15 and y = 8. When you graph the intersecting lines, the intersection is (x,y) which is (15, 8) as the point of intersection and ONLY SOLUTION to the system, and NOT (8,15). Try plotting (15, 8) and its different from (8,15).