The solution to the system of equations is . What is the value of ?

Solution available with step-by-step explanation

SAT Systems of Two Linear Equations Question 88 | Free SAT Prep | Aniko

00:00

Question 88·Easy·Systems of Two Linear Equations in Two Variables

0 / 140

$x = 2$

$3x + y = 11$

The solution to the system of equations is $(x, y)$ . What is the value of $y$ ?

For systems where one equation already gives a variable (like $x = 2$ ), immediately use substitution: plug that value into the other equation, simplify carefully, and solve the resulting one-variable equation. This avoids unnecessary graphing or elimination, reduces algebra steps, and minimizes arithmetic mistakes—just be precise with operations when isolating the remaining variable.

Hints

Click me!

Use the equation that is already solved for a variable

One of the equations already gives you $x$ directly. Use that to help with the other equation.

Substitute into the other equation

Take the value of $x$ from the first equation and plug it into $3x + y = 11$ wherever you see $x$ .

Solve the resulting simple equation

After substitution, you will have an equation with just $y$ . Rearrange it to isolate $y$ on one side.

Desmos Guide

Enter the two equations

In Desmos, type x = 2 on one line to graph the vertical line, and 3x + y = 11 on another line (or solve for $y$ and enter y = 11 - 3x).

Find the intersection point

Look for the point where the two graphs intersect. Click that point to see its coordinates; the $y$ -coordinate of this intersection is the value of $y$ you need.

Step-by-step Explanation

Identify which equation to substitute into

You are given a system of two equations:

$x = 2$
$3x + y = 11$

Since the first equation already tells you the value of $x$ , you can substitute this directly into the second equation.

Substitute $x=2$ into the second equation

Replace $x$ with $2$ in the equation $3x + y = 11$ :

3(2) + y = 11

Now simplify $3(2)$ .

Simplify and solve for $y$

Compute $3(2)$ to get $6$ , so the equation becomes

6 + y = 11

To isolate $y$ , subtract $6$ from both sides:

\begin{aligned} 6 + y - 6 &= 11 - 6 \\ y &= 5 \end{aligned}

So, the value of $y$ is $5$ , which corresponds to answer choice B.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation