how many solutions does this linear system have? one solution: (8, 0)one solution: (0, 8)no solutioninfinite number of solutions

Solve the second equation for y

x+2y = -8
x+2y-x = -8-x
2y = -x-8
2y/2 = -x/2 -8/2
y = (-1/2)x - 4

The slope here is -1/2, which is the same slope as the first equation. Because of this fact and the fact that the y intercept is not the same, we have two parallel lines. The parallel lines never cross. 

There are no solutions