The system of equations is If is the solution to the system, what is the value of ?

Solution available with step-by-step explanation

SAT Systems of Two Linear Equations Question 10 | Free SAT Prep | Aniko

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Question 10·Easy·Systems of Two Linear Equations in Two Variables

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The system of equations is

4x - 2y = 10

y = x - 1

If $(x,y)$ is the solution to the system, what is the value of $x$ ?

Your answer

(Express the answer as an integer)

When solving a system of two linear equations and one is already solved for a variable (for example, $y = \text{expression in }x$ ), use substitution: plug that expression into the other equation, simplify carefully, and solve the resulting one-variable equation. Pay close attention to distributing negative signs and combining like terms, since small arithmetic mistakes are the most common reason for wrong answers on these straightforward substitution problems.

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Pick the easier equation to work with

One of the equations already tells you $y$ in terms of $x$ . Use that to avoid dealing with two variables at once.

Use substitution

Take the expression for $y$ from the second equation and plug it into the first equation everywhere you see $y$ .

Solve the resulting one-variable equation

After substituting, simplify the equation step by step: distribute, combine like terms, and then isolate $x$ by using inverse operations.

Desmos Guide

Enter the two equations

In Desmos, type 4x - 2y = 10 on one line and y = x - 1 on another line so both lines are graphed.

Find the intersection point

Look for the point where the two lines cross. You can tap or click on the intersection point; Desmos will display its coordinates $(x, y)$ .

Use the x-coordinate as your answer

Read the x-coordinate of the intersection point shown by Desmos. That x-value is the solution to the system and is what you should enter as your answer.

Step-by-step Explanation

Use the equation already solved for y

The second equation is already solved for $y$ :

y = x - 1

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

Substitute into the first equation

Start with the first equation:

4x - 2y = 10

Substitute $y = x - 1$ into this equation:

4x - 2(x - 1) = 10

Now you have an equation with only $x$ .

Simplify the equation in terms of x

Distribute the $-2$ across the parentheses:

4x - 2(x - 1) = 4x - 2x + 2

So the equation becomes:

4x - 2x + 2 = 10

Combine like terms:

2x + 2 = 10

Now solve this simpler linear equation for $x$ .

Solve for x and state the solution

From the equation

2x + 2 = 10

subtract 2 from both sides:

2x = 8

Then divide both sides by 2:

x = 4

So, the value of $x$ that makes both equations true is 4.

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