Problem:
How many ordered pairs of real numbers satisfy the following system of equations?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The graph of the first equation is a parabola opening downward with vertex ( 0,3 ), passing through and . The second equation is satisfied if either or . Therefore the graph of the second equation is a square with vertices , and together with a square with vertices , and . As shown below, the two graphs intersect at (\text{D})\boxed{5} points- , , and 2 points on the larger square in the lower half-plane.
The problems on this page are the property of the MAA's American Mathematics Competitions