do the Two systems of equations shown have the same solution?

Question

4x+y=−1
x+y=2

8x+2y=−2
−4x+2y=−8

Answer 1

Yes, the two systems of equations have the same solution. The first system of equations can be solved by adding the two equations, resulting in:

4x + y + x + y = -1 + 2
5x + 2y = 1

Solving the second system of equations also by adding the two equations will result in the same equation:

8x + 2y + (-4x) + 2y = -2 + (-8)
4x + 4y = -10

So, both systems of equations lead to the equation 5x + 2y = 1, indicating that they have the same solution.