To solve the system of equations:

\[
y = 2x - 18 \quad \text{(1)}
\]
\[
y = x + 6 \quad \text{(2)}
\]

We can use the substitution or elimination method. Here, I'll use substitution since both equations are already in the form of \( y = \).

### Step-by-step Solution:
1. From equation (2), we already have \( y = x + 6 \).
2. Substitute \( y = x + 6 \) into equation (1):
   \[
   x + 6 = 2x - 18
   \]
3. Solve for \( x \):
   \[
   6 + 18 = 2x - x
   \]
   \[
   24 = x
   \]
   So, \( x = 24 \).

4. Substitute \( x = 24 \) back into equation (2) to find \( y \):
   \[
   y = 24 + 6 = 30
   \]

### Solution:
The solution to the system of equations is:
\[
x = 24, \quad y = 30
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the graphical representation of this system of equations?
2. How do we solve this using the elimination method?
3. Can you solve a system of equations with three variables?
4. How do substitution and elimination methods differ?
5. What happens if the system has no solutions?

**Tip**: For quick checks, substitute the solution back into both original equations to verify if it satisfies them both.

Learn how to solve the system of linear equations y = 2x - 18 and y = x + 6 using the substitution method. This step-by-step solution covers key algebraic concepts and is suitable for students in Grades 8-10.

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