Determine if the equations are parallel, perpendicular, or neither

x + y = 8 and y = - x - 1

Because we have a value of y we can plug it into the original equation.

x + (-x - 1) = 8

x - x - 1 = 8

Combine like terms.

-1 = 8

Add 1 to both sides.

0 ≠ 9

The equations are parallel because they do not have a common solution.