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

Where are the following equations?