The ordered pair satisfies the system of equations above. What is the value of ?

Solution available with step-by-step explanation

SAT Systems of Two Linear Equations Question 74 | Free SAT Prep | Aniko

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Question 74·Medium·Systems of Two Linear Equations in Two Variables

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\begin{cases} y = 7 - 3x \\[4pt] 2x + y = -4 \end{cases}

The ordered pair $(x, y)$ satisfies the system of equations above. What is the value of $y$ ?

Your answer

(Express the answer as an integer)

When one equation in a system already isolates a variable (like $y = 7 - 3x$ ), use substitution to save time: plug that expression into the other equation so you only have one variable, solve it carefully, then substitute back to find the other variable. Watch your signs when combining like terms and subtracting, and double-check that you are giving the variable the question actually asks for (here, $y$ , not $x$ ).

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Choose a method

One equation already has $y$ by itself. How could you use that to replace $y$ in the other equation?

Make it a one-variable equation

Take $y = 7 - 3x$ and plug it into the equation $2x + y = -4$ . What equation in terms of $x$ only do you get?

Solve and back-substitute

After you solve for $x$ , go back to the equation $y = 7 - 3x$ and substitute your $x$ value to find $y$ .

Desmos Guide

Enter the first equation

In Desmos, type the first equation as y = 7 - 3x. This will graph the first line.

Enter the second equation

On the next line, type the second equation exactly as 2x + y = -4. Desmos will graph this line as well.

Find the intersection point

Tap or click on the point where the two lines intersect. Look at the ordered pair shown; the second number (the $y$ -coordinate) is the value of $y$ that solves the system.

Step-by-step Explanation

Substitute for y in the second equation

The first equation already gives $y$ in terms of $x$ :

y = 7 - 3x

Substitute $7 - 3x$ for $y$ in the second equation $2x + y = -4$ :

2x + (7 - 3x) = -4

Now you have an equation with only $x$ .

Solve the equation for x

Simplify and solve for $x$ :

\begin{aligned} 2x + 7 - 3x &= -4 \\ -x + 7 &= -4 \\ -x &= -11 \\ x &= 11 \end{aligned}

Now that you know $x$ , you can find $y$ using the first equation.

Substitute x back to find y

Use $y = 7 - 3x$ and plug in $x = 11$ :

\begin{aligned} y &= 7 - 3(11) \\ y &= 7 - 33 \\ y &= -26 \end{aligned}

So, the value of $y$ is $-26$ .

Strategy

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Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation