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 92 | Free SAT Prep | Aniko

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Question 92·Medium·Systems of Two Linear Equations in Two Variables

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\begin{cases} 2x + 3y = 17 \\ x - y = 1 \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)

For systems of two linear equations, first look for the equation where a variable has coefficient 1 or -1, and solve that equation for that variable to minimize fractions. Use substitution to plug this expression into the other equation, then carefully distribute and combine like terms to get a simple one-variable equation. Solve, and if needed, substitute back to check your work; this approach is quick and reduces algebra mistakes on SAT problems like this.

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Pick the easier equation

Look at the equation $x - y = 1$ . Can you rearrange it so that either $x$ or $y$ is alone on one side?

Use substitution

Once you have $x$ written in terms of $y$ (or $y$ in terms of $x$ ), replace that variable in the other equation with your expression so that the equation has only one variable.

Be careful with distribution

When you substitute into $2x + 3y = 17$ , remember that $x$ is an expression. Use parentheses and distribute the 2 correctly before combining like terms and solving for $y$ .

Desmos Guide

Graph the first equation

Type y = (17 - 2x) / 3 into Desmos to graph the line that represents the equation $2x + 3y = 17$ .

Graph the second equation

On a new line, type y = x - 1 to graph the line that represents the equation $x - y = 1$ .

Find the intersection

Look at the point where the two lines intersect. The y-coordinate of this intersection point is the value of $y$ that solves the system.

Step-by-step Explanation

Solve one equation for a variable

Start with the simpler equation:

x - y = 1

Solve for $x$ by adding $y$ to both sides:

x = y + 1

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

Substitute into the other equation

Substitute $x = y + 1$ into the first equation $2x + 3y = 17$ :

2(y + 1) + 3y = 17

Distribute and combine like terms:

2y + 2 + 3y = 17 \\[0.7em] 5y + 2 = 17

Now you have an equation with just $y$ .

Solve for y

Solve the one-variable equation:

5y + 2 = 17 \\[0.7em] 5y = 15 \\[0.7em] y = 3

So, the value of $y$ is $3$ .

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