A system of equations asks for points that satisfy both equations. A squared plus a squared signals a circle, and a line can cross a circle more than once. Graph both equations as written in Desmos and click every intersection. Then read each point in order; a point on the circle alone may not satisfy the line.
Hints
- Hint 1
A solution to a system is a point that makes both equations true. What does tell you about the second coordinate compared with the first?
- Hint 2
The equation draws a circle, not a filled region. Add the line to its graph and look for every place they cross.
Step-by-step
Graph both equations and read the crossings
Step 1Use the line to check coordinate order
Since , the second coordinate of each answer point must be greater than the first. An intersection is a point shared by two graphs, so each answer point must lie on both the circle and the line.
- Step 2
Graph the circle
Type as written. Desmos draws a circle centered at that reaches units in each direction, since . Don't add in front; that would change the equation.
- Step 3
Click both intersections
Add on a new line. Click both places where the line crosses the circle. Desmos shows and . At each point, is greater than , and the point is on the circle. These are the requested coordinates. Choice A.