To solve this equation, we can start by isolating one variable in one of the equations and substituting it into the other equation.

From the first equation, x + 1 = 100, we can isolate x by subtracting 1 from both sides:

x = 100 - 1
x = 99

Now we can substitute this value of x into the second equation:

25 = y - x
25 = y - 99

To isolate y, we can add 99 to both sides:

25 + 99 = y - 99 + 99
124 = y

Therefore, the solution to the system of equations is x = 99 and y = 124.