Club A has 17 members and Club B has 25 members. If there is a total of 38 people that belong to the two clubs, how many people belong to both clubs?

I know the answer and the steps required to solve it but I'm uncertain about why those steps are necessary.

X = both clubs

Club B has 25 - x ... u take the total and subtract the ones that are in both

Club A has 17 - x ... same here ^

x + (25 - x) + (17 - x) = 38 ... so both + club B + club A = total

-2x + x + 42 = 38

-x = 38 - 42

-x = - 4

x = 4 ... so there are 4 members that belong to both clubs <==

so there are 17 - 4 = 13 in club A only

and 25 - 4 = 21 in club B only

4 in both

13 + 21 + 4 = 38

38 = 38 (correct)

answer is : 4 in both