The two squared variables signal a circle, while an equation of the form graphs a line. Type both equations into Desmos and count their intersections, the points they share. Each intersection gives an ordered pair that satisfies both equations. Don’t stop at the first crossing or count points that sit on only one graph.
Hints
- Hint 1
The equation with both coordinates squared graphs a circle. Desmos accepts the whole circle equation as written; you don’t need to rewrite it starting with . What does the other equation graph?
- Hint 2
A solution to a system must satisfy both equations. On the graph, look where the line meets the circle, not where either graph meets an axis. How many shared points are there?
Step-by-step
Count the graph intersections
Step 1Graph the circle
The squared and in describe a circle: the squared distance from is at every point on it. Type exactly as given, without adding . Desmos draws the circle.
- Step 2
Count where the line meets the circle
Type on the next line. Desmos draws a line; click its crossings with the circle to see and . An ordered pair lists a point’s -coordinate first, then its -coordinate. Each shared point satisfies both equations, so these two crossings give exactly two real ordered pairs. Choice C.
Lessons that teach this
- SAT Advanced AlgebraAdvancedCoreSolve linear and nonlinear systems
- SAT Advanced AlgebraIntermediateUse the quadratic formula and discriminant
- SAT Geometry and TrigonometryBeginnerRead and write circle equations
- DesmosIntermediateCoreCircle equations in the graph
- DesmosIntermediateCoreHow many solutions?