Final answer:
The system of equations is solved using the elimination method, yielding the ordered pair (-4, 5) as the solution.
Step-by-step explanation:
Using the elimination method to solve the system of equations, we want to find the correct ordered pair that satisfies both equations. We have:
x - 3y = -19 (1)
2x + y = -3 (2)
Firstly, we multiply equation (2) by 3 so we can eliminate y by adding it to equation (1):
6x + 3y = -9 (2')
Now we add equations (1) and (2'):
x - 3y + 6x + 3y = -19 + (-9)
7x = -28
Divide both sides by 7:
x = -4
With x found, we can substitute it back into one of the original equations to find y. Let's use equation (2):
2(-4) + y = -3
-8 + y = -3
Add 8 to both sides:
y = 5
Thus, the correct ordered pair is (-4, 5).