To solve the system of equations using substitution, we first have the following two equations:
- \( y = -6x + 9 \)
- \( y = -4x + 5 \)
Since both equations are equal to \( y \), we can set them equal to each other:
\[ -6x + 9 = -4x + 5 \]
Next, we will solve for \( x \):
- Move \( -4x \) to the left side:
\[ -6x + 4x + 9 = 5 \]
This simplifies to:
\[ -2x + 9 = 5 \]
- Now, subtract 9 from both sides:
\[ -2x = 5 - 9 \]
\[ -2x = -4 \]
- Divide by -2:
\[ x = \frac{-4}{-2} = 2 \]
Now that we have the value of \( x \), we substitute it back into one of the original equations to find \( y \). We'll use the first equation:
\[ y = -6(2) + 9 \]
Calculating this gives:
\[ y = -12 + 9 = -3 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (2, -3) \]
So, the final answer is:
\[ \boxed{(2, -3)} \]