A linear-nonlinear system can pair a line with a circle; the squared variables signal the curved graph. Graph both equations as written in Desmos and count their intersections, since each shared point makes both equations true. Look at the whole graph before counting: a point on only one graph is not a solution.
Hints
- Hint 1
A system needs both equations to be true at once. Graph the line first. Its points satisfy the first equation, but which of those points also satisfy the equation with squares?
- Hint 2
The equation with squared and draws a circle. Where it crosses the line, the same ordered pair works in both equations. Count shared points, not points that lie on only one graph.
Step-by-step
Count intersections in Desmos
Step 1Graph the line
Type in Desmos. It draws a straight line containing every point that satisfies the first equation. A point on this line is a solution to the system only if it also satisfies the second equation.
- Step 2
Count the points shared with the circle
Add on the next line. Desmos draws a circle. Click where it meets the line to see and . An intersection lies on both graphs, so each intersection is one distinct ordered pair satisfying the system. Negative coordinates count because they are real numbers. There are exactly two such pairs. Choice D.