A squared paired with a straight-line equation signals a nonlinear system: a curve and a line. Graph both equations in Desmos and click their shared point. That point gives the ordered pair because it satisfies both equations. The line may only touch the curve, so don’t look only for a visible crossing or accept a point on one graph alone.
Hints
- Hint 1
The term makes one graph a parabola, a U-shaped curve. Type that equation exactly as given; changing the constant term changes where the curve sits.
- Hint 2
An intersection is a point on both graphs. Add the line to Desmos and look for where it meets the parabola, even if the graphs touch without crossing.
Step-by-step
Graph both equations and click their shared point
Step 1Graph the parabola
Type into Desmos. The term makes its graph a parabola, a U-shaped curve. Keep the term when you type it; changing that term moves the curve.
- Step 2
Find the point on both graphs
Type on the next line. Desmos draws a line that touches the parabola; click the touching point to see . An intersection belongs to both graphs, so a system’s solution must satisfy both equations. The requested ordered pair is . Choice C.