First consider the equalities: x=-3, so y=-24 and -9+y=15, y=24. This gives us some boundaries for y: -24<=y<=24. As x increases from -3, the boundaries for y decrease. For example, when x=0, -9<=y<=15. In this example, x+y has a maximum value of 15. When x=2, 1<=y<=9 and the maximum for x+y is 11, and when x=3, 6<=y<=6, so y=6 and x+y=9. Now we have restrictions on x: -3<=x<=3. Therefore, we need to select the lowest value of x, which is -3 and the highest value for y, which is 24, making the maximum of x+y=-3+24=21.