https://file.aiquickdraw.com/mathbot/file/1729787108973odc161gu.jpg

We have the following system of equations from the image:

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

To find the value of \( x \), we can substitute the expression for \( y \) from the second equation into the first equation.

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

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

### Step 2: Simplify the equation
Distribute the -5 on the left side:

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

### Step 3: Combine like terms
\[
28x - 160 = 22
\]

### Step 4: Solve for \( x \)
Add 160 to both sides:

\[
28x = 182
\]

Now, divide by 28:

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

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

Would you like further details or clarifications on any step?

### Related questions:
1. How do you check if the solution for \( x \) is correct?
2. What is the value of \( y \) after finding \( x \)?
3. How can you solve the system using the elimination method?
4. Can this system of equations be solved graphically, and what would the intersection represent?
5. How does substitution differ from other methods like elimination in solving systems of equations?

### Tip:
When solving systems of equations, substitution is particularly useful when one equation is already solved for one variable.

Felicia has the following system of equations: 3x - 5y = 22 and y = -5x + 32. What is the value of x in the solution to this system?

Learn how to solve the system of equations 3x - 5y = 22 and y = -5x + 32 using the substitution method. A detailed step-by-step solution is provided, covering key algebraic concepts and the substitution theorem. Suitable for students in Grades 8-10.

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