A nonlinear system can pair a line with a circle, and the two graphs may meet more than once. Graph both equations as written in Desmos and click every intersection. Each shared point satisfies both equations. If Desmos shows decimals but the choices use fractions, match the coordinates carefully; changing a coordinate’s sign gives a different point.
Hints
- Hint 1
A solution to a system is a point that makes both equations true. On a graph, it must lie on both the line and the circle. Look for every place the graphs meet.
- Hint 2
An intersection may appear in Desmos with decimal coordinates even when the choices use fractions. Convert each coordinate without changing its sign before you compare the points.
Step-by-step
Graph both equations and match the points
Step 1Find every shared point
Type and on separate lines in Desmos. Click both places where the line crosses the circle. Desmos shows and approximately . Each intersection lies on both graphs, so it satisfies both equations. Stopping at the first point would miss a solution.
- Step 2
Match the decimals to exact coordinates
The choices write the negative coordinates as fractions. Convert them without dropping either minus sign:
So the two ordered pairs are and . Choice D.