To solve the system of equations by substitution, we have the following equations:
- \( y = 9x \) (Equation 1)
- \( y = 3x - 24 \) (Equation 2)
Since both equations equal \( y \), we can set them equal to each other:
\[ 9x = 3x - 24 \]
Next, we will isolate \( x \). First, subtract \( 3x \) from both sides:
\[ 9x - 3x = -24 \]
This simplifies to:
\[ 6x = -24 \]
Now, divide both sides by 6:
\[ x = -4 \]
Now that we have the value of \( x \), we can substitute it back into Equation 1 to find the value of \( y \):
\[ y = 9x \]
Substituting \( x = -4 \):
\[ y = 9(-4) = -36 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-4, -36) \]
So, the final answer is: \[ \boxed{(-4, -36)} \]
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