A nonlinear system has at least one equation with a curve, such as one containing . Graph both equations in Desmos and click their intersections; each shared point makes both equations true. If the question asks for all ordered pairs, don't stop at the first crossing or switch the coordinates.
Hints
- Hint 1
The term makes one graph a parabola, a U-shaped curve. A line can cross a parabola twice, so looking at only one crossing might miss a solution.
- Hint 2
An intersection lies on both graphs, so its coordinates satisfy both equations. Type each equation as given, then click the crossings. In each ordered pair, the first coordinate is .
Step-by-step
Graph both equations and read the intersections
Step 1Read the first shared point
Type and on separate Desmos lines. Click the crossing on the right; Desmos shows . An intersection lies on both graphs, so this point satisfies both equations. The curve can cross the line again, so don't stop here.
- Step 2
Read the other point and keep both
Click the crossing on the left; Desmos shows . An ordered pair puts before . Because the question asks for all solutions, keep both crossings in that order. The solutions are and . Choice D.