To solve the system of equations using the elimination method, we start with the two equations given:
- \( 3y + 9x = 24 \)
- \( -4y + 8x = 28 \)
We want to eliminate one of the variables. Let's multiply the first equation by 4 and the second equation by 3 so that the coefficients of \(y\) will match:
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\( 4(3y + 9x) = 4 \cdot 24 \) \[ 12y + 36x = 96 \]
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\( 3(-4y + 8x) = 3 \cdot 28 \) \[ -12y + 24x = 84 \]
Now we have the new system of equations:
- \( 12y + 36x = 96 \)
- \( -12y + 24x = 84 \)
Next, we add the two equations together to eliminate \(y\):
\[ (12y + 36x) + (-12y + 24x) = 96 + 84 \] \[ 0y + 60x = 180 \]
This simplifies to:
\[ 60x = 180 \]
Now, divide both sides by 60:
\[ x = \frac{180}{60} = 3 \]
Now that we have \(x\), we substitute it back into one of the original equations to find \(y\). We can use the first equation:
\[ 3y + 9(3) = 24 \] \[ 3y + 27 = 24 \] \[ 3y = 24 - 27 \] \[ 3y = -3 \] \[ y = \frac{-3}{3} = -1 \]
So the solution to the system of equations is:
\[ (x, y) = (3, -1) \]
Thus, the ordered pair solution is:
\[ \boxed{(3, -1)} \]
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