We start with the given system of equations: \[ \begin{align_} y &= 4x - 9 \quad (1) \\ y &= x - 3 \quad (2) \end{align_} \]
Since both equations equal \( y \), we can set them equal to each other: \[ 4x - 9 = x - 3 \]
Rearranging the equation to isolate \( x \): \[ 4x - x = -3 + 9 \\ 3x = 6 \\ x = \frac{6}{3} = 2 \]
Now that we have \( x = 2 \), we substitute it back into either equation to find \( y \). Using equation (2): \[ y = 2 - 3 = -1 \]
The solution to the system of equations is: \[ \begin{align_} x &= 2 \\ y &= -1 \end{align_} \]
\(\boxed{(x, y) = (2, -1)}\)
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