Question 264·Medium·Algebra

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The system of equations below has solution $(x, y)$ .

\begin{aligned} x &= 2y - 1 \\[1.4em] 3x + y &= 11 \end{aligned}

Which choice gives the value of $x$ ?

A system of equations asks for values that make two equations true at once. When the equations use the same $x$ and $y$ , graph both as written in Desmos and click their intersection. Desmos gives an ordered pair $(x,y)$ ; read the coordinate the question asks for. Reversing the two coordinates is the main trap.

Hints

Hint 1
A solution to a system makes both equations true. Each equation graphs as a line. What point belongs to both lines?
Hint 2
An ordered pair $(x,y)$ lists $x$ first and $y$ second. After you click where the lines cross, which coordinate does the question ask you to report?

Step-by-step

Graph the system and read the point
Step 1
Identify what solves both equations
In this system, the same $x$ and $y$ must make both equations true. Each equation graphs as a line, so their intersection is the solution $(x,y)$ . A point on only one line might fail the other equation.
Step 2
Click the intersection and read $x$
Type $x=2y-1$ and $3x+y=11$ on separate Desmos lines. Click their intersection; Desmos shows $(3,2)$ . In the ordered pair $(x,y)$ , $x$ is the first coordinate, so the value of $x$ is $3$ . Choice B.

Question 264·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

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