Question

question 7 of 10
how many solutions does the nonlinear system of equations graphed below have?
graph of a circle and a line intersecting
click here for long description
a. zero
b. one
c. two
d. four

Explanation:

Step1: Recall solution definition

The solutions of a system of equations (linear or nonlinear) graphed are the points of intersection of their graphs.

Step2: Analyze the graph

The graph shows a circle (nonlinear) and a line (linear). By observing the intersection points, we can see that the line intersects the circle at two distinct points? Wait, no, wait. Wait, looking at the graph (from the description: the line and the circle—wait, maybe I misread. Wait, the user's graph: the line intersects the circle at two points? Wait, no, wait the options: A. Zero, B. One, C. Two, D. Four. Wait, maybe the line intersects the circle at two points? Wait, no, wait the graph: let's re-examine. The circle and the line: how many times do they cross? From the diagram (as per the user's image), the line intersects the circle at two points? Wait, no, wait maybe I made a mistake. Wait, no—wait, the problem is a nonlinear system (circle is nonlinear, line is linear). The solutions are the intersection points. So count the number of intersection points. Looking at the graph, the line intersects the circle at two points? Wait, no, wait the options: C is Two. Wait, but let me check again. Wait, maybe the line touches the circle at two points? Wait, the graph: the circle and the line—so the number of intersection points is two? Wait, no, wait the options: C. Two. So the answer should be C.

Answer:

C. Two