A nonlinear system has two equations sharing variables, with a squared variable making one graph a curve. Graph both equations as written in Desmos, then click a crossing to read its ordered pair: that point lies on both graphs. Don't stop after checking the line; a solution must also lie on the curve.
Hints
- Hint 1
An ordered pair lists the -value first and the -value second. For a system, the same pair must work in both equations. What point on the two graphs would do that?
- Hint 2
The graph of is a U-shaped parabola, while gives a line. Where they cross, both equations describe the same point. Click a crossing and compare its coordinates to the choices.
Step-by-step
Find a shared point on the graph
Step 1Graph both equations
Type and on separate Desmos lines. Desmos shows a U-shaped parabola and a line crossing twice. Each crossing lies on both graphs, so its coordinates satisfy both equations.
- Step 2
Read the matching ordered pair
Click the right-hand crossing. Desmos labels it , meaning and . This point appears among the choices, and its position on both graphs means it solves both equations. A solution to a system must satisfy both equations. Choice D.