Question 109·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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Consider the system of equations:

\begin{aligned} x^2 + y^2 &= 25 \\[1.4em] y &= 3 \end{aligned}

What is one possible value of $x$ ?

A nonlinear system has two equations that must be true for the same pair of values; a squared variable is the cue here. When one equation gives a variable outright, substitute that value into the other, then solve the resulting equation in Desmos. Watch the square on $x$ : finding $x^2$ isn't the same as finding $x$ .

Hints

Hint 1
A solution is a pair of values that satisfies both equations. The second equation already tells you what $y$ is. Put that value in place of $y$ in the first equation.
Hint 2
The question asks for $x$ , not $x^2$ . A positive number and its negative have the same square, so the equation may give two possible values. You only need one that appears among the choices.

Step-by-step

Substitute, then solve in Desmos
Step 1
Use the given value of y
A solution must satisfy both equations. Since the second equation gives $y=3$ , put $3$ in place of $y$ in the first equation:
$x^2+3^2=25.$
Now there's only one unknown, $x$ .
Step 2
Find one possible x-value
Type $x_{1}^{2}+3^{2}\sim25\{x_{1}>0\}$ in Desmos. Use $x_{1}$ so Desmos solves for a number rather than graphs $x$ ; the regression symbol $\sim$ asks it to make the sides match. The positive restriction selects one possible sign. Under PARAMETERS, Desmos shows $x_{1}=4$ . So $x=4$ , together with $y=3$ , satisfies the system. Give the value of $x$ , not the value of $x^2$ . Choice C.

Question 109·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