Question 142·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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Consider the system of equations

\begin{aligned} \sqrt{x+9} &= y \\[1.4em] y &= 4 \end{aligned}

Which value of $x$ satisfies the system?

A system of equations asks for values that make both equations true. If one equation fixes $y$ , put that value into the other equation to see what $x$ must satisfy. In Desmos, graph the two original equations and click where they meet. Read the coordinate the question asks for, not a value you reached partway through solving.

Hints

Hint 1
A solution to a system must make both equations true. If one equation sets $y$ to a number, what happens when you replace $y$ with that number in the other equation?
Hint 2
The graph of $y=4$ is a horizontal line: every point on it has second coordinate $4$ . Find where it meets the square-root curve, then read the first coordinate for $x$ .

Step-by-step

Graph the two equations
Step 1
Connect the two equations
The second equation fixes $y$ at $4$ . A system solution must satisfy both equations at the same point. So look for the point where the graph of $y=4$ meets the graph of $y=\sqrt{x+9}$ .
Step 2
Read the intersection’s x-coordinate
Type both original equations into Desmos: $y=\sqrt{x+9}$ and $y=4$ . Click where the graphs meet; Desmos shows $(7,4)$ . In a point $(x,y)$ , the first coordinate is $x$ , so the value of $x$ satisfying the system is $7$ . Choice A.

Question 142·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