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 97 | Free SAT Prep | Aniko

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Question 97·Easy·Systems of Two Linear Equations in Two Variables

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The system of equations is

\begin{cases} x + y = 12 \\ x - y = 4 \end{cases}

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

Your answer

(Express the answer as an integer)

For systems like this, quickly scan for a variable that can be eliminated by adding or subtracting the equations. Here, the $+y$ and $-y$ make addition ideal: add the equations to cancel $y$ , solve the resulting one-variable equation, and, if needed, plug back into either original equation to check. Practicing this pattern—spotting opposite coefficients and using elimination—saves time and reduces arithmetic mistakes on the SAT.

Hints

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Look at how the equations are similar

Compare the two equations: one has $+y$ and the other has $-y$ . Think about what happens if you add the equations together.

Try to eliminate a variable

Your goal is to get an equation with just $x$ . Which operation on the two equations (adding or subtracting) will make the $y$ terms disappear?

Solve the resulting one-variable equation

After you eliminate $y$ , you will get an equation involving only $x$ . Solve that equation carefully and check your arithmetic.

Desmos Guide

Enter the first equation as a line

In Desmos, type y = 12 - x to represent the equation $x + y = 12$ (solved for $y$ ).

Enter the second equation as a line

Type y = x - 4 to represent the equation $x - y = 4$ (also solved for $y$ ). You should now see two lines on the graph.

Find the intersection point

Click or tap where the two lines intersect. Desmos will show the coordinates $(x, y)$ of that point; the x-coordinate of this intersection is the value of $x$ that solves the system.

Step-by-step Explanation

Choose a method to solve the system

You are given the system:

$x + y = 12$

$x - y = 4$

Notice that one equation has $+y$ and the other has $-y$ . This makes the elimination method (adding the equations to cancel $y$ ) very convenient.

Add the two equations to eliminate $y$

Add the left sides together and the right sides together:

\begin{aligned} (x + y) + (x - y) &= 12 + 4 \\ 2x &= 16 \end{aligned}

The $+y$ and $-y$ cancel out, leaving an equation with only $x$ .

Solve for x

From the equation $2x = 16$ , divide both sides by 2:

$x = \dfrac{16}{2} = 8$ .

So, the value of $x$ is 8.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation