Final answer:
To solve the system of equations using elimination, we add the two equations to cancel out x and then solve for y and subsequently for x, resulting in the solution x = -3, y = -2.
Step-by-step explanation:
To solve the system using elimination, you have two equations: 2x+3y=-12 and -2x+y=4.
Step 1: Add the two equations together. This will eliminate the x variable since 2x and -2x cancel each other out.
Result of addition: 3y + y = -12 + 4
Simplify: 4y = -8
Step 2: Divide both sides of the equation by 4 to isolate y.
y = -8 / 4
Solve for y: y = -2
Step 3: Substitute y = -2 into one of the original equations to solve for x.
Using the second equation -2x + y = 4:
-2x + (-2) = 4
Solve for x: -2x = 4 + 2
-2x = 6
Divide both sides by -2 to get x:
x = -3
The solution to the system of equations is x = -3, y = -2.