To solve the given system of equations using elimination, we have:
- \(-3x + y = -9\) (Equation 1)
- \(x - 2y = -12\) (Equation 2)
First, we can manipulate these equations to eliminate one of the variables.
Let's rearrange both equations to work with easier coefficients:
From Equation 1: \[ y = 3x - 9 \]
From Equation 2: \[ x = 2y - 12 \]
Now, let's manipulate one of the original equations for elimination. We can multiply Equation 1 by 2 to align the coefficients of \(y\):
Multiply Equation 1 by 2: \[ -6x + 2y = -18 \quad \text{(Equation 3)} \]
Now we have:
- \( -6x + 2y = -18 \) (Equation 3)
- \( x - 2y = -12 \) (Equation 2)
Now we can add Equation 3 and Equation 2 together:
\[ (-6x + 2y) + (x - 2y) = -18 - 12 \] This simplifies to: \[ -6x + x + 2y - 2y = -30 \] \[ -5x = -30 \] \[ x = 6 \]
Now we can substitute \(x = 6\) back into one of the original equations to find \(y\). Let's use Equation 1: \[ -3(6) + y = -9 \] \[ -18 + y = -9 \] \[ y = -9 + 18 \] \[ y = 9 \]
The solution to the system of equations is: \[ (x, y) = (6, 9) \]
Thus, the solution in your answer choices is: (6, 9).