Final answer:
The solution to the system of linear equations 2x + y = -4 and 2x + 3y = -12 is the ordered pair (0, -4) found using the elimination method.
Step-by-step explanation:
To determine which ordered pair is the solution of the system of linear equations 2x + y = -4 and 2x + 3y = -12, one can use the method of substitution or elimination to solve the equations. Since the coefficient of x is the same in both equations, the elimination method is suitable here. First, you want to eliminate one of the variables by subtracting one equation from the other. Let's subtract the first equation from the second:
- 2x + 3y = -12
- -(2x + y = -4)
When you subtract the first equation from the second, you get:
Divide both sides by 2 to find y:
Once you find the value of y, substitute it back into one of the original equations to find x:
Divide both sides by 2:
Therefore, the solution to the system of equations is the ordered pair (0, -4).