To solve the system of equations using elimination, we start with the given equations:
- \( 4x - 6y = -48 \)
- \( -2x + 4y = 30 \)
Let's first align them for easier manipulation:
\[ 4x - 6y = -48 \quad (1) \] \[ -2x + 4y = 30 \quad (2) \]
To eliminate one of the variables, we can multiply equation (2) by a factor that will allow us to add or subtract it from equation (1) to eliminate one of the variables.
We can multiply equation (2) by 2:
\[ 2(-2x + 4y) = 2(30) \]
This gives us:
\[ -4x + 8y = 60 \quad (3) \]
Now, we will add equations (1) and (3):
- \( 4x - 6y = -48 \)
- \( -4x + 8y = 60 \)
Adding the two equations:
\[ (4x - 4x) + (-6y + 8y) = -48 + 60 \] \[ 0 + 2y = 12 \] \[ 2y = 12 \] \[ y = 6 \]
Now that we have \( y = 6 \), we can substitute this value back into one of the original equations to solve for \( x \). We'll use equation (1):
\[ 4x - 6(6) = -48 \] \[ 4x - 36 = -48 \] \[ 4x = -48 + 36 \] \[ 4x = -12 \] \[ x = -3 \]
The solution to the system of equations is:
\[ (x, y) = (-3, 6) \]
The correct answer from the given options is:
(−3, 6)