Question

Solve the system of equations:

-4x - 2y = -12
4x + 8y = -24
Options:
A) (-2, 8)
B) (-6, 6)
C) (6, -6)
D) (8, -2)

Answer 1

To solve the system of equations -4x - 2y = -12 and 4x + 8y = -24, use the method of elimination to eliminate one variable and solve for the other. The solution is (x, y) = (12, -18).

Step-by-step explanation:

To solve the given system of equations:
-4x - 2y = -12
4x + 8y = -24

We can use the method of elimination to eliminate one variable and solve for the other. Here's how:

1. First, multiply the first equation by 2 to make the coefficients of 'y' in both equations opposite each other.
2. The new system of equations becomes:
   -8x - 4y = -24
   4x + 8y = -24
3. Add the two equations together to eliminate 'y':
   -8x - 4y + 4x + 8y = -24 + (-24)
   -4x = -48
4. Divide both sides of the equation by -4 to solve for 'x':
   x = -48 / -4
   x = 12
5. Substitute the value of 'x' back into either of the original equations to solve for 'y'. Using the first equation:
   -4(12) - 2y = -12
   -48 - 2y = -12
   -2y = -12 + 48
   -2y = 36
   y = 36 / -2
   y = -18

Therefore, the solution to the system of equations is (x, y) = (12, -18).