To solve this system of equations, we can use either substitution or elimination method.

Let's use the elimination method.

Given equations:
1) 2x + y = 25
2) x + y = 4

We can subtract the second equation from the first equation to eliminate the variable y:

(2x + y) - (x + y) = 25 - 4
2x + y - x - y = 21
x = 21

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

x + y = 4
21 + y = 4
y = 4 - 21
y = -17

Therefore, the solution to the system of equations is:
x = 21
y = -17