To solve the system of equations using the substitution method, we will substitute the expression for \( y \) from one equation into the other.
We have the two equations:
- \( y = 10x - 9 \)
- \( y = x + 18 \)
Since both equations are equal to \( y \), we can set them equal to each other:
\[ 10x - 9 = x + 18 \]
Now, we'll solve for \( x \):
- First, subtract \( x \) from both sides:
\[ 10x - x - 9 = 18 \]
\[ 9x - 9 = 18 \]
- Next, add 9 to both sides:
\[ 9x = 27 \]
- Now, divide by 9:
\[ x = 3 \]
Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use \( y = x + 18 \):
\[ y = 3 + 18 = 21 \]
So the solution is \( (3, 21) \).
The correct ordered pair is:
\((3, 21)\)