AMC 10 A

Answer (D): The graph of the first equation is a parabola opening downward with vertex $(0, 3)$, passing through $(-3, 0)$ and $(3, 0)$. The second equation is satisfied if either $|x| + |y| = 5$ or $|x| + |y| = 3$. Therefore the graph of the second equation is a square with vertices $(5, 0)$, $(0, 5)$, $(-5, 0)$, and $(0, -5)$ together with a square with vertices $(3, 0)$, $(0, 3)$, $(-3, 0)$, and $(0, -3)$. As shown below, the two graphs intersect at 5 points—$(0, 3)$, $(3, 0)$, $(-3, 0)$, and 2 points on the larger square in the lower half-plane.