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

Solution available with step-by-step explanation

SAT Systems of Two Linear Equations Question 61 | Free SAT Prep | Aniko

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Question 61·Easy·Systems of Two Linear Equations in Two Variables

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The system of equations is

\begin{cases} 3x - y = 5 \\ x = 4 \end{cases}

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

For systems where one equation already gives you a variable (like $x = 4$ ), use substitution immediately: plug that value into the other equation so you have a single-variable equation. Then solve step by step, watching signs carefully. This is usually faster and less error-prone than graphing or trying to combine the equations using elimination on simple SAT questions like this.

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Start with the easier equation

One of the equations already gives you $x$ directly. Use that first before working with the other equation.

Substitute for x

Take the value of $x$ from the second equation and plug it into $3x - y = 5$ so that the only variable left is $y$ .

Isolate y carefully

After substituting, simplify the multiplication, then use inverse operations (adding or subtracting on both sides, then dividing or multiplying if needed) to get $y$ alone. Pay close attention to negative signs.

Desmos Guide

Enter the equations in Desmos

Type the first equation in Desmos as y = 3x - 5 (this is just rewriting $3x - y = 5$ by solving for $y$ ). Then type the second equation as x = 4.

Find the intersection point

Look at the graph and find the point where the line y = 3x - 5 intersects the vertical line x = 4. The $y$ -coordinate of this intersection point is the value of $y$ in the solution $(x, y)$ .

Step-by-step Explanation

Use the simpler equation

From the second equation, we already know the exact value of $x$ :

x = 4

This value must be used in the first equation to find $y$ .

Substitute into the first equation

Take $x = 4$ and plug it into the first equation $3x - y = 5$ :

3(4) - y = 5

Now simplify $3(4)$ .

Solve for $y$

First compute $3(4)$ :

12 - y = 5

Subtract 12 from both sides:

-y = 5 - 12 = -7

Multiply both sides by $-1$ :

y = 7

So the value of $y$ in the solution $(x, y)$ is $7$ .

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Step-by-step Explanation

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Step-by-step Explanation