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.