Question

Apex Precal please help

How many solutions are there for the system shown below?

2x^2+y^2=33
x^2+y^2+2y=19

A. 1
B. 4
C. 3
D. 2

Answer 1

Your answer for this question will be B.4

Answer 2

Choice B; 4

Explanation:

The solution to a system of equations is a pair of points (x, y) such that both equations pass through the given point. The number of solutions will thus be the number of such points where both functions pass through or intersect. The solutions to a system of equations can be determined analytically or graphically.

In this case, the graphical approach is much easier to use. We simply graph the two equations on the same graph and determine the number of points where they intersect.

From the attachment below, we see that the functions intersect at 4 distinct points. Hence there are 4 solutions to the system of equations given.