Final answer:
The solution set for the given system of equations by elimination is (x, y) = (-3, 1).
Step-by-step explanation:
The solution set of the system 2x−2y=−8 and x+2y=−1 using the elimination method can be found by adding the two equations together. When we do this, the y terms cancel out because -2y and +2y add up to zero. This leaves us with the equation 3x=−9. Solving for x gives us x=−3. To find y, we can substitute x=−3 into one of the original equations, for example, the second equation: x+2y=−1 becomes (−3)+2y=−1. Solving for y we get 2y=2, which simplifies down to y=1. Therefore, the solution set is (−3, 1).