Question 220·Medium·Nonlinear Equations in One Variable; Systems in Two Variables

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The system of equations below is given.

\begin{aligned} x^2 + y^2 &= 25 \\[1.4em] y &= x + 1 \end{aligned}

What is one possible value of $x$ ?

A nonlinear system has two equations in the same unknowns, with at least one graph that curves. Graph both equations as written in Desmos and click where they meet; each intersection satisfies both equations. If the question asks for $x$ , read the first coordinate of an intersection, not its $y$ -coordinate or a point on only one graph.

Hints

Hint 1
A system asks for a point that satisfies both equations. The curved equation draws a circle, and the other draws a line. Where would you look for a point that lies on both?
Hint 2
An intersection is where two graphs meet. Click each meeting point and read its coordinates in the order $(x,y)$ . Which coordinate gives the value of $x$ ?

Step-by-step

Graph both equations
Step 1
Find where the graphs meet
Type $x^2+y^2=25$ and $y=x+1$ on separate Desmos lines. Desmos draws a circle and a line with two crossings. Each crossing is a point that makes both equations true.
Step 2
Read the requested coordinate
Click both crossings. Desmos shows $(-4,-3)$ and $(3,4)$ . In each point $(x,y)$ , $x$ comes first. The $4$ in $(3,4)$ is its $y$ -value, so one possible value of $x$ is $3$ . Choice C.

Question 220·Medium·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