Which one of the following is a description of the graph of the solution set for the system below?
$$x^{2}+y^{2} \geq 36$$
$$4 x^{2}+9 y^{2} \geq 36$$
A) The area inside the ellipse (defined by the second equation), including the border.
B) The area outside the ellipse (defined by the second equation), including the border.
C) The area outside the circle (defined by the first equation), including the border.
D) None of these

Question

Quizplus · Accepted Answer

The first equation $x^{2}+y^{2} \geq 36$ describes all the points at or outside the circle with radius 6 centered at the origin. The second equation $4x^{2}+9y^{2} \geq 36$ describes an ellipse, but it does not restrict the solution set further since the question asks for the description of the graph of the solution set for the system, not the individual characteristics of each equation. The correct description is the area outside the circle defined by the first equation, including the border, which matches choice C.

Which One of the Following Is a Description of the Graph