2. 
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?
A.‒6.5

B.0.5

C.6.5

D.‒0.5


We are given the system of equations:

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

To solve this system, we can use substitution. Since the second equation already gives \( y \) in terms of \( x \), we can substitute \( y = -5x + 32 \) into the first equation.

### Step 1: Substitute the second equation into the first equation
\[
3x - 5(-5x + 32) = 22
\]

### Step 2: Simplify the equation
Distribute the \( -5 \):
\[
3x + 25x - 160 = 22
\]
\[
28x - 160 = 22
\]

### Step 3: Solve for \( x \)
Add 160 to both sides:
\[
28x = 182
\]

Divide both sides by 28:
\[
x = \frac{182}{28} = 6.5
\]

### Final Answer:
The value of \( x \) is \( 6.5 \), so the correct answer is **C. 6.5**.

Would you like to go over any details or have further questions?

Here are some related questions to deepen your understanding:

1. What is the value of \( y \) in the solution to the system of equations?
2. How would you solve the system of equations using the elimination method?
3. What happens if you graph both equations? Where do they intersect?
4. Can a system of equations have no solution? How would that be represented?
5. How does substitution compare to elimination when solving systems of equations?

**Tip:** Always check your solution by plugging the value of \( x \) back into both original equations to verify the result.

Felicia has the following system of equations on her math homework: 3x−5y=22 and y= ‒5x+32. What is the value of x in the solution to this system of equations? A.‒6.5 B.0.5 C.6.5 D.‒0.5

Discover how to solve a system of linear equations using the substitution method with the problem 3x−5y=22 and y=‒5x+32. Step-by-step solution provided for students in Grades 8-10, focusing on key algebraic concepts and substitution techniques.

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