A system with a line and a circle can have more than one solution because the graphs can meet in two places. In Desmos, graph each equation as written and click their intersections, the points that satisfy both. Then read the coordinate the question asks for, not the circle’s radius or the other coordinate.
Hints
- Hint 1
A system asks for values that make both equations true at once. A point on the circle satisfies the first equation, but it must also lie on the line. Where would a point on both graphs appear?
- Hint 2
An intersection is a point two graphs share. Type the circle equation as written, without putting in front, then add the line on another Desmos line and click the crossings.
- Hint 3
A point written lists the -coordinate first. After you click an intersection, which number in the point answers the question? You need only one value that works.
Step-by-step
Graph the circle and line
Step 1Graph the circle as written
Type into Desmos. It draws a circle, showing the points that satisfy the first equation. Don’t add in front: that would change the equation. You still need the line to find points that satisfy both.
- Step 2
Read an intersection’s x-coordinate
Add and click both intersections. Desmos shows and . At an intersection, both equations hold. The -coordinate is the first number in a point, so gives . The is its -coordinate, not the value asked for. One possible value of is . Choice D.