SAT Systems of Two Linear Equations Question 89 | Free SAT Prep | Aniko

00:00

Question 89·Medium·Systems of Two Linear Equations in Two Variables

0 / 140

\begin{cases} y = 4x - 1 \\ 2x + y = 17 \end{cases}

In the solution to the system of equations above, what is the value of $x$ ?

For systems of linear equations on the SAT, first check if one equation is already solved for a variable (like $y = 4x - 1$ here). If so, substitution is usually fastest: plug that expression into the other equation, combine like terms, and solve the resulting one-variable equation. Always do a quick plug-back check (mentally or on paper) to make sure your $x$ (and $y$ if needed) satisfy both original equations, which also helps catch sign or arithmetic mistakes.

Hints

Click me!

Notice what is already solved for you

Look at the first equation. One of the variables is already written in terms of the other. How can that help you with the second equation?

Replace $y$ in the second equation

In the second equation, try substituting the expression from the first equation for $y$ so that the second equation has only $x$ in it.

Solve the one-variable equation

After substituting, combine like terms, isolate $x$ , and then simplify to find its value.

Desmos Guide

Enter both equations

In Desmos, type the first equation exactly as given: y = 4x - 1 on one line. For the second equation, solve for $y$ first: from $2x + y = 17$ , get $y = 17 - 2x$ , and enter that as y = 17 - 2x on another line.

Find the intersection point

Look for the point where the two lines intersect on the graph. Click on that intersection point; Desmos will show its coordinates $(x, y)$ . The $x$ -coordinate of this point is the value of $x$ that solves the system.

Step-by-step Explanation

Use the equation already solved for $y$

The first equation is already solved for $y$ :

y = 4x - 1

This means wherever you see $y$ in the second equation, you can replace it with $4x - 1$ .

Substitute into the second equation

Take the second equation

2x + y = 17

and substitute $y = 4x - 1$ :

2x + (4x - 1) = 17

Now you have an equation with only $x$ .

Solve for $x$

Combine like terms on the left:

\begin{aligned} 2x + 4x - 1 &= 17 \\ 6x - 1 &= 17 \end{aligned}

Add 1 to both sides:

6x = 18

Divide both sides by 6:

x = 3

So, in the solution to the system, the value of $x$ is $3$ . This corresponds to answer choice B.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation