What ordered pair satisfies the system of equations?

Solution available with step-by-step explanation

SAT Systems of Two Linear Equations Question 79 | Free SAT Prep | Aniko

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Question 79·Easy·Systems of Two Linear Equations in Two Variables

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

\begin{aligned} x + y &= 5\\ x - y &= 1 \end{aligned}

For a system of two linear equations, quickly check if adding or subtracting the equations will eliminate one variable—this is often faster than solving for a variable and substituting. Here, adding the equations cancels $y$ immediately, giving $x$ in one step; then substitute that $x$ -value into either original equation to find $y$ , and finally match the ordered pair to the options, verifying it satisfies both equations.

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Look for a way to combine the equations

Notice that one equation has $+y$ and the other has $-y$ . What happens to $y$ if you add the two equations together?

Find $x$ first

After you add the equations and the $y$ terms cancel, you will get an equation with only $x$ . Solve that equation to find the value of $x$ .

Plug back in to find $y$

Once you know $x$ , substitute it into either $x + y = 5$ or $x - y = 1$ to solve for $y$ . Then match that ordered pair to the answer choices.

Desmos Guide

Enter the first equation

In the expression line, type y = 5 - x to represent the equation $x + y = 5$ rewritten as $y = 5 - x$ .

Enter the second equation

In a new line, type y = x - 1 to represent the equation $x - y = 1$ rewritten as $y = x - 1$ .

Find the intersection point

Look at the graph where the two lines intersect and tap/click the intersection point; read off the coordinates shown. That coordinate pair is the solution to the system and should match one of the answer choices.

Step-by-step Explanation

Combine the equations to eliminate a variable

We have the system:

\begin{aligned} x + y &= 5 \\ x - y &= 1 \end{aligned}

Add the two equations term by term:

(x + y) + (x - y) = 5 + 1

On the left side, $+y$ and $-y$ cancel, leaving:

2x = 6

Solve for $x$

From $2x = 6$ , divide both sides by $2$ :

x = \frac{6}{2} = 3

So the $x$ -coordinate of the solution is $3$ .

Substitute to find $y$ and identify the ordered pair

Substitute $x = 3$ into one of the original equations, for example $x + y = 5$ :

3 + y = 5

Subtract $3$ from both sides:

y = 2

So the solution that satisfies both equations is the ordered pair $(3,2)$ , which corresponds to answer choice B.

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Step-by-step Explanation

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Step-by-step Explanation