Felicia has the following system of equations on her math homework.
 
3x−5y=22
y= ‒5x+32

What is the value of x
 in the solution to this system of equations?

We are given the following system of equations:

1. \( 3x - 5y = 22 \)
2. \( y = -5x + 32 \)

To find the value of \( x \), we can use substitution since the second equation already expresses \( y \) in terms of \( x \).

### Step 1: Substitute \( y = -5x + 32 \) into the first equation.

\[
3x - 5(-5x + 32) = 22
\]

### Step 2: Distribute the \(-5\) across the terms inside the parentheses.

\[
3x + 25x - 160 = 22
\]

### Step 3: Combine like terms.

\[
28x - 160 = 22
\]

### Step 4: Add 160 to both sides to isolate the \( x \)-term.

\[
28x = 182
\]

### Step 5: Solve for \( x \) by dividing both sides by 28.

\[
x = \frac{182}{28} = 6.5
\]

So, the value of \( x \) is \( \boxed{6.5} \).

Would you like to see how to find the corresponding value of \( y \), or do you have any other questions?

### Related Questions:
1. How do we solve for \( y \) in this system?
2. How can you verify the solution for both \( x \) and \( y \)?
3. Can you solve this system using the elimination method?
4. How do you graphically represent the solution of this system of equations?
5. What if the second equation were \( y = 5x - 32 \), how would the solution change?

**Tip:** Substitution works best when one of the equations is already solved for one variable, making it easier to substitute and simplify.

Felicia has the following system of equations on her math homework.
3x−5y=22
y=‒5x+32
What is the value of x in the solution to this system of equations?

Learn how to solve the system of linear equations 3x - 5y = 22 and y = -5x + 32 using the substitution method. Follow a step-by-step guide to find the value of x, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation