x + y = 8

Question

y = 1/3x + 4

Answer 1

x + y = 8

y = 1/3x + 4

x + 1/3x + 4 = 8

1 1/3x = 4

x = 3

Answer 2

when you typed
1/3x + 4
I assume you mean (1/3)x + 4
and not 1/(3x) + 4
or 1/(3x+4)

y = (8-x)
so
(8-x) = (1/3) x + 4

24 - 3 x = x + 12

4 x = 12

x = 3