To figure this out, let's use substitution and try to find values for x and y.
x + 1 = -x + 5
2x + 1 = 5
2x = 4
x = 2
y = x + 1
y = 2 + 1
y = 3
(2, 3)
3 = 2 + 1
3 = 3
3 = -2 + 5
3 = 3
Yes, there is a solution to both of these linear pair equations.
Hope this helps!! :)