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?

Group of answer choices

-6.5

0.5

6.5

-0.5

We are given the following system of equations:

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

To solve for \( x \), we'll substitute the expression for \( y \) from the second equation into the first equation.

### 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:

\[
28x = 182
\]

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

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

Thus, the value of \( x \) is \( 6.5 \).

The correct answer is:
**6.5**

Would you like further details or explanations?

Here are five related questions to deepen your understanding:

1. How can you check if your solution is correct by substituting back into both equations?
2. What is the value of \( y \) corresponding to \( x = 6.5 \)?
3. What is substitution method in solving systems of equations?
4. What other methods can be used to solve systems of equations, besides substitution?
5. How can you tell if a system of equations has no solution or infinitely many solutions?

**Tip:** Always double-check your solutions by plugging the values of the variables back into the original equations.

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?

Group of answer choices

-6.5
0.5
6.5
-0.5

Learn how to solve the system of linear equations 3x - 5y = 22 and y = -5x + 32 using the substitution method. This problem covers key algebraic concepts, such as solving systems of equations and linear equations. Ideal for students in Grades 8-10.

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