What ordered pair satisfies the following system of equations?

Solution available with step-by-step explanation

SAT Systems of Two Linear Equations Question 52 | Free SAT Prep | Aniko

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Question 52·Easy·Systems of Two Linear Equations in Two Variables

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What ordered pair $(x, y)$ satisfies the following system of equations?

\begin{cases} 3x + 2y = 16\\ x - y = 2 \end{cases}

For systems of two linear equations on the SAT, quickly scan for an equation where a variable has coefficient $1$ or $-1$ (like $x - y = 2$ ). Isolate that variable, substitute into the other equation to get a single-variable equation, solve it, then back-substitute to find the other variable. Finally, verify mentally that your ordered pair satisfies both original equations before choosing the answer.

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Use the easier equation first

Focus on $x - y = 2$ . Can you rearrange it so that $x$ is alone on one side, or $y$ is alone on one side?

Substitute into the other equation

Once you have $x$ in terms of $y$ (or $y$ in terms of $x$ ), replace that variable in the equation $3x + 2y = 16$ with your expression.

Solve step by step

After substituting, you should have an equation with only one variable. Solve it carefully, then plug that value back into one of the original equations to find the other variable.

Desmos Guide

Graph both equations

In Desmos, enter 3x + 2y = 16 on one line and x - y = 2 on another line. Desmos will draw both lines on the same coordinate plane.

Find the intersection point

Look for the point where the two lines cross. Tap or click that intersection point; Desmos will display its coordinates. Those coordinates give the $(x, y)$ pair that satisfies both equations.

Step-by-step Explanation

Isolate a variable from the simpler equation

Look at the equation $x - y = 2$ . This is easy to solve for one variable.

Solve for $x$ in terms of $y$ :

x - y = 2 \\[0.7em] x = y + 2

Now you have $x$ written in terms of $y$ .

Substitute into the other equation

Use the expression $x = y + 2$ in the first equation $3x + 2y = 16$ .

Substitute $y + 2$ for $x$ :

3x + 2y = 16 \\[0.7em] 3(y + 2) + 2y = 16

Distribute and combine like terms:

3y + 6 + 2y = 16 \\[0.7em] 5y + 6 = 16

Now solve for $y$ :

5y = 10 \\[0.7em] y = 2

Back-substitute to find the other variable

Now that you know $y = 2$ , plug this into $x = y + 2$ :

x = y + 2 \\[0.7em] x = 2 + 2 \\[0.7em] x = 4

So the solution to the system is the ordered pair $(x, y) = (4, 2)$ , which corresponds to answer choice D.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation