Final answer:
To find the solution to the given system of linear equations, we add both equations to eliminate the x-variable, finding y = -6. Then we substitute y = -6 back into one of the equations to get x = 6. Hence, the solution is C. (6,-6).
Step-by-step explanation:
Solution to the System of Linear Equations
To solve the given system of linear equations, which consists of:
- -4x - 2y = -12
- 4x + 8y = -24
We can start by adding both equations to eliminate the x-variable:
- (-4x - 2y) + (4x + 8y) = -12 + (-24)
- -2y + 8y = -12 - 24
- 6y = -36
Dividing both sides by 6 yields y = -6. To find x, substitute y back into either of the original equations. Let's use the first equation:
- -4x - 2(-6) = -12
- -4x + 12 = -12
- -4x = -24
Dividing both sides by -4 yields x = 6. Therefore, the solution to the system of equations is (6, -6).
The correct answer is C. (6,-6).