Consider the system of equations: What is the value of ?

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SAT Systems of Two Linear Equations Question 127 | Free SAT Prep | Aniko

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Question 127·Easy·Systems of Two Linear Equations in Two Variables

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Consider the system of equations:

\begin{cases} 2x + y = 11 \\ x - y = 1 \end{cases}

What is the value of $x$ ?

For systems of two linear equations, first check if adding or subtracting the equations will quickly eliminate a variable (as when one equation has $+y$ and the other has $-y$ ). Use elimination in that case to get a simple one-variable equation, solve it, and then (if needed) substitute back to verify. This is usually faster and less error-prone on the SAT than doing more complicated substitution unless the system is already solved for a variable.

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Look for a quick way to remove one variable

Compare the two equations and focus on the $y$ terms. Is there a way to combine the equations so that $y$ disappears?

Try adding the equations

What happens to $y$ if you add $2x + y = 11$ and $x - y = 1$ together, left side with left side and right side with right side?

Solve the resulting one-step equation

After you add the equations, you should get an equation with only $x$ . Solve that simple equation to find the value of $x$ .

Desmos Guide

Enter both lines in Desmos

Type the two equations in slope-intercept form:

For $2x + y = 11$ , solve for $y$ to get $y = 11 - 2x$ and enter that.
For $x - y = 1$ , solve for $y$ to get $y = x - 1$ and enter that.

Find the intersection point

On the graph, locate the point where the two lines cross. Tap or hover over the intersection to see its coordinates; the $x$ -coordinate of this point is the value of $x$ in the system.

Step-by-step Explanation

Choose a method to eliminate a variable

Look at the system:

\begin{cases} 2x + y = 11 \\ x - y = 1 \end{cases}

Notice that one equation has $+y$ and the other has $-y$ . If you add the two equations, the $y$ terms will cancel out. This is the elimination method.

Add the equations to get an equation in $x$ only

Add the left sides together and the right sides together:

Left sides: $(2x + y) + (x - y) = 2x + y + x - y = 3x$ (the $y$ terms cancel).
Right sides: $11 + 1 = 12$ .

So you get:

3x = 12

Solve for $x$ and match the answer choice

Solve $3x = 12$ by dividing both sides by $3$ :

x = \frac{12}{3} = 4

So the value of $x$ is $4$ , which corresponds to answer choice C.

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Desmos Guide

Step-by-step Explanation

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Desmos Guide

Step-by-step Explanation