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

To solve this system of equations, we can use substitution since the second equation is already solved for \( y \). 

Here are the given equations:
1. \( 3x - 5y = 22 \)
2. \( y = -5x + 32 \)

### Step 1: Substitute the expression for \( y \) from the second equation into the first equation.

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

### Step 2: Distribute the \( -5 \) across \( -5x + 32 \).

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

### Step 3: Combine like terms.

\[
28x - 160 = 22
\]

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

\[
28x = 182
\]

### Step 5: Divide both sides by 28 to solve for \( x \).

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

### Final Answer:
The value of \( x \) is \( 6.5 \).

The correct answer is **6.5**.

Do you need further details or have any questions?

Here are some related questions you might want to explore:
1. How do you check the solution for both \( x \) and \( y \)?
2. What are the steps for solving a system of equations using substitution?
3. Can this system of equations be solved using the elimination method?
4. What happens if both equations are in standard form instead of one being solved for \( y \)?
5. How does the slope of the second equation affect the graph of the solution?

**Tip:** Always substitute your solution back into the original equations to verify its accuracy.

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?

Explore how to solve a system of equations using the substitution method with the equations 3x – 5y = 22 and y = ‒5x + 32. This detailed, step-by-step solution is ideal for students in Grades 8-10 and includes core algebraic concepts.

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