x + y = 8

y = 1/3x + 4

x + y = 8

y = 1/3x + 4

x + 1/3x + 4 = 8

1 1/3x = 4

x = 3

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

To solve the system of equations:

1. Substitute the value of y from the second equation into the first equation.
- Since y = 1/3x + 4, substitute it into the first equation: x + (1/3x + 4) = 8

2. Simplify the expression by combining like terms. Distribute the 1/3 through the parentheses.
- x + 1/3x + 4 = 8
- (3/3)x + (1/3)x + 4 = 8
- (4/3)x + 4 = 8

3. Subtract 4 from both sides of the equation to isolate the term with x.
- (4/3)x + 4 - 4 = 8 - 4
- (4/3)x = 4

4. Multiply both sides of the equation by 3/4 to solve for x.
- (3/4)(4/3)x = (3/4)(4)
- x = 3

5. Substitute the value of x back into either equation to find the value of y.
- Using the second equation, y = 1/3(3) + 4 = 1 + 4 = 5

So, the solution to the system of equations is x = 3 and y = 5.