To solve the system of equations:
- \(-9x + y = 12\)
- \(2x + 4y = -28\)
We can solve one of the equations for one variable and then substitute it into the other equation.
Let's start with the first equation:
\[ y = 9x + 12 \]
Now, we will substitute \(y\) in the second equation:
\[ 2x + 4(9x + 12) = -28 \]
Now, distribute the \(4\):
\[ 2x + 36x + 48 = -28 \]
Combine like terms:
\[ 38x + 48 = -28 \]
Now, subtract \(48\) from both sides:
\[ 38x = -28 - 48 \] \[ 38x = -76 \]
Now, divide by \(38\):
\[ x = \frac{-76}{38} = -2 \]
Now that we have \(x\), we substitute it back to find \(y\):
\[ y = 9(-2) + 12 \] \[ y = -18 + 12 \] \[ y = -6 \]
So the solution to the system of equations is:
\[ \boxed{(-2, -6)} \]
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