A nonlinear system can pair a line with a curve; a squared term is the cue that the graphs might meet more than once. Graph both equations in Desmos and click each intersection, where the graphs meet. Each intersection is one solution, so all solutions means every shared point. Stopping at the first crossing can leave out a valid point.
Hints
- Hint 1
An intersection is a point on both graphs, so its coordinates make both equations true. The squared term makes one graph a curve rather than a line. Could the line cross it in more than one place?
- Hint 2
An ordered pair lists first and second. Click each place where the graphs meet, and record both coordinates before choosing a set of solutions.
Step-by-step
Graph and collect the intersections
Step 1Find the first shared point
The squared term makes the first graph a parabola, a U-shaped curve. Type and on separate Desmos lines. Click the left intersection, where the graphs meet. Desmos labels it , so that pair satisfies both equations.
- Step 2
Find the other point and give the full set
Click the other intersection. Desmos labels it . An ordered pair gives both coordinates of one solution, and the question asks for all of them. Keep both points: . Choice A.