Question 194·Hard·Nonlinear Equations in One Variable; Systems in Two Variables

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4x + y = 29

y = 50 - x^2

The graphs of the equations in this system intersect at the point $(x, y)$ in the $xy$ -plane. What is a possible value of $x$ ?

Two equations in $x$ and $y$ , with one squared term, signal a nonlinear system: a line and a curve may meet more than once. Graph both equations in Desmos and click their intersections. Read the $x$ -coordinate, the first number in each point. An $x$ -value works only if both equations give the same $y$ -value.

Hints

Hint 1
A solution to a system must satisfy both equations at once. On a graph, where would a point have to be to belong to both equations?
Hint 2
The $x^2$ term makes a parabola, a curved graph that can cross a line twice. Check both crossings, then read the first coordinate of a crossing point.

Step-by-step

Graph the two equations
Step 1
Find where the graphs meet
Type $4x+y=29$ and $y=50-x^2$ on separate Desmos lines. You see a line and a parabola, the curve made by the squared $x$ , crossing twice. At a crossing, the same point satisfies both equations. So either crossing could give the requested $x$ -value.
Step 2
Read the requested coordinate
Click both crossings. Desmos labels the points $(-3,41)$ and $(7,1)$ . In a point written $(x,y)$ , the first number is $x$ . So $-3$ and $7$ are possible $x$ -values, and $-3$ is the one offered. Choice D.

Question 194·Hard·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