To solve the system of equations using elimination, we start with the two equations:
- \( 4x - 6y = -48 \)
- \( -2x + 4y = 30 \)
Step 1: Align the equations
We have: \[ 4x - 6y = -48 \tag{1} \] \[ -2x + 4y = 30 \tag{2} \]
Step 2: Multiply the equations if necessary
We want to eliminate one of the variables. Let's eliminate \( x \) by making the coefficients of \( x \) the same. To do this, we can multiply the second equation by \( 2 \) to match the coefficient of \( x \) in the first equation:
\[ 2(-2x + 4y) = 2(30) \] This gives us: \[ -4x + 8y = 60 \tag{3} \]
Step 3: Add the equations
Now we can add equation (1) and the modified equation (3): \[ (4x - 6y) + (-4x + 8y) = -48 + 60 \] This simplifies to: \[ 2y = 12 \] Now, divide both sides by \( 2 \): \[ y = 6 \]
Step 4: Substitute \( y \) back into one of the original equations to find \( x \)
We can substitute \( y = 6 \) back into the first equation: \[ 4x - 6(6) = -48 \] This simplifies to: \[ 4x - 36 = -48 \] Now, add \( 36 \) to both sides: \[ 4x = -48 + 36 \] \[ 4x = -12 \] Now, divide by \( 4 \): \[ x = -3 \]
Solution
The solution to the system of equations is \( (x, y) = (-3, 6) \).
Thus, the correct answer is (−3, 6).