To solve the system of equations using elimination with multiplication, we start with the given equations:
- \(4x - 6y = -48\)
- \(-2x + 4y = 30\)
To eliminate one variable, we will manipulate both equations. We can multiply the second equation by 2 to align the \(x\) coefficients:
Multiply the second equation by 2: \[ 2(-2x + 4y) = 2(30) \] This gives us: \[ -4x + 8y = 60 \quad \text{(3)} \]
Now we have the transformed system of equations:
- \(4x - 6y = -48\)
- \(-4x + 8y = 60\)
Next, we can add equations (1) and (3) together to eliminate \(x\):
\[ (4x - 6y) + (-4x + 8y) = -48 + 60 \] This simplifies to: \[ (4x - 4x) + (-6y + 8y) = 12 \] \[ 0 + 2y = 12 \] \[ 2y = 12 \] \[ y = 6 \]
Now that we have \(y = 6\), we can substitute this value back into one of the original equations to find \(x\). Let's substitute into equation (1):
\[ 4x - 6(6) = -48 \] \[ 4x - 36 = -48 \] \[ 4x = -48 + 36 \] \[ 4x = -12 \] \[ x = -3 \]
Thus, the solution to the system of equations is \(x = -3\) and \(y = 6\). The solution is:
\[ (-3, 6) \]
So the correct answer is \(( -3, 6 )\).