The phrase “satisfies both equations” signals a system: one ordered pair must work in each equation. For a circle paired with a line, graph both equations as written in Desmos and click where they cross. A point can lie on the circle but fail the line, so don’t check only one graph.
Hints
- Hint 1
A solution to a system is a point on both graphs. One equation draws a circle and the other draws a line. Where would a point have to be to belong to both?
- Hint 2
Desmos can graph the circle equation as written, without solving it for . Type each equation on its own line, then look for the places where the circle and line cross.
Step-by-step
Graph both equations
Step 1Identify what a solution must do
The word both makes this a system: one ordered pair must fit both equations. The first graph is a circle, and the second is a line. A solution is where their graphs meet, not merely a point on the circle.
- Step 2
Graph the circle and line
Type and on separate lines in Desmos. It draws both graphs. Their two crossings are intersections, places where the same point fits both equations.
- Step 3
Read the matching intersection
Click each intersection. Desmos labels them and . An ordered pair lists first and second; only appears among the choices. That point satisfies both equations. Choice D.