SAT Linear Equations in Two Variables Question 131 | Free SAT Prep

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Question 131·Hard·Linear Equations in Two Variables

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Solve the following system of equations. What is the value of $x+y$ ?

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

For a two-variable linear system, use substitution when one equation can be rearranged quickly for a variable. Substitute that expression into the other equation, solve for one variable, find the other, and then calculate exactly what the question asks for.

Hints

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Use the simpler equation first

Rearrange $x-y=2$ to write either $x$ or $y$ in terms of the other variable.

Substitute

Replace that variable in $3x+2y=16$ with the expression you found.

Find the requested expression

After solving for both variables, add their values rather than selecting the value of just one variable.

Desmos Guide

Graph both equations

Enter $3x+2y=16$ and $x-y=2$ on separate Desmos lines.

Find the intersection

Click the point where the two lines intersect to read the solution coordinates.

Add the coordinates

Add the intersection point's $x$ -coordinate and $y$ -coordinate to verify the requested value.

Step-by-step Explanation

Express one variable in terms of the other

From $x-y=2$ , add $y$ to both sides:

x=y+2

Substitute into the first equation

Substitute $y+2$ for $x$ in $3x+2y=16$ :

\begin{aligned} 3(y+2)+2y&=16\\ 5y+6&=16\\ 5y&=10\\ y&=2 \end{aligned}

Find the requested sum

Since $x=y+2$ , $x=2+2=4$ . Therefore,

x+y=4+2=6

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