To solve this system of equations using the method of addition, we need to first make one of the variables cancel out when the equations are added together.

Given the equations:
1) 3u - 5v = 20
2) u + v = 4

First, let's multiply the second equation by 5 to match the coefficients of v in both equations:

5(u + v) = 5(4)
5u + 5v = 20

Now, we can add this new equation to the first equation:

(3u - 5v) + (5u + 5v) = 20 + 20
8u = 40

Divide by 8 on both sides to solve for u:

u = 40 / 8
u = 5

Now that we have the value of u, we can substitute it back into one of the original equations to solve for v:

5 + v = 4
v = 4 - 5
v = -1

Therefore, the solution to the system of equations is u = 5 and v = -1.