Question 76·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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If $(x, y)$ is a solution to the system of equations below, which of the following is a possible value of $x$ ?

\begin{cases} x + y = 8 \\ x^2 - y = 12 \end{cases}

A nonlinear system has two equations in the same variables, with a squared term signaling a curve rather than a second line. Graph both equations in Desmos and click their intersections: each point must satisfy both equations at once. The graphs may meet more than once, so read the coordinate the question asks for before choosing an answer.

Hints

Hint 1
An intersection is a point on both graphs, so its coordinates satisfy both equations. Enter the equations as written in Desmos; you don't need to solve either one for $y$ first.
Hint 2
In a point $(x,y)$ , the first coordinate is $x$ . If the graphs meet twice, click both intersections. Which first coordinate appears among the choices?

Step-by-step

Read the intersections in Desmos
Step 1
Graph both equations
Type $x+y=8$ and $x^2-y=12$ on separate Desmos lines, without rearranging them. The squared $x$ makes the second graph a parabola, a U-shaped curve. Desmos shows two crossings, so check both: each crossing lies on both graphs.
Step 2
Read the requested coordinate
Click both intersections. Desmos shows $(-5,13)$ and $(4,4)$ . An $x$ -coordinate is the first number in a point $(x,y)$ , so the possible $x$ -values are $-5$ and $4$ . The question asks for a possible value of $x$ , so choose $4$ . Read the requested coordinate, not the whole point. Choice C.

Question 76·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this