https://file.aiquickdraw.com/mathbot/file/1729189099051umo8mhek.jpg

Let's solve the system of equations provided in the image:

\[
x + 3y = 1
\]
\[
y = -x + 15
\]

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

We know:
\[
y = -x + 15
\]

Substitute this into the first equation:
\[
x + 3(-x + 15) = 1
\]

### Step 2: Simplify the equation.

Distribute the \( 3 \):
\[
x - 3x + 45 = 1
\]
\[
-2x + 45 = 1
\]

### Step 3: Solve for \( x \).

Move the constant to the other side:
\[
-2x = 1 - 45
\]
\[
-2x = -44
\]

Divide both sides by \(-2\):
\[
x = 22
\]

### Conclusion:
The solution for \( x \) is \( 22 \), which corresponds to option **C**.

---

Would you like further details on this solution or any related questions?

Here are five related questions you could explore:
1. How can you solve the same system of equations using graphing?
2. What is the value of \( y \) once \( x = 22 \)?
3. How can we check if the solution satisfies both original equations?
4. What are alternative methods for solving systems of equations like substitution and elimination?
5. What happens when two lines in a system of equations are parallel?

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

Solve the following system of equations for x: x + 3y = 1 and y = -x + 15.

Learn how to solve the system of equations x + 3y = 1 and y = -x + 15 using substitution. This step-by-step solution simplifies the equations to find that x = 22. Suitable for students in Grades 9-11.

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