Final answer:
The solution to the system of inequalities involves graphing both an ellipse and an area above an exponential function and finding their intersection.
Step-by-step explanation:
The question posed involves finding the graph that represents the solution to a system of inequalities. The system given is a quadratic inequality, x2 + 4y2 < 64, in conjunction with an exponential inequality, y > 3x. To graph this system, we need to recognize the first inequality as representing the interior of an ellipse (since x2 and y2 are both positive values and are added together), and the second inequality as the region above the graph of an exponential function.
The solution set would then be where these two regions intersect. The ellipse represented by x2 + 4y2 < 64 is centered at the origin with a radius of 8 along the x-axis and a radius of 4 along the y-axis. The inequality y > 3x represents the area above the exponential curve y=3x, which tends to rise very steeply for positive values of x.