To solve the system of equations given by:
- \( y = -6x + 3 \)
- \( y = -9x + 9 \)
we can set the two equations equal to each other since they both equal \( y \):
\[ -6x + 3 = -9x + 9 \]
Next, we will solve for \( x \):
- Add \( 9x \) to both sides:
\[ -6x + 9x + 3 = 9 \]
This simplifies to:
\[ 3x + 3 = 9 \]
- Subtract 3 from both sides:
\[ 3x = 6 \]
- Divide by 3:
\[ x = 2 \]
Now that we have \( x \), we can substitute it back into either equation to find \( y \). We will use the first equation:
\[ y = -6(2) + 3 \]
Calculating this gives:
\[ y = -12 + 3 = -9 \]
Thus, the solution to the system of equations is:
\[ \boxed{(2, -9)} \]