which is correct as a title: "The river system and the water supply" or "the river system and water supply"? And would you remove all determiners and leave it like this: "River system and water supply"?
In English, adjectives can be "reused" in a pattern like A (B1 C1) and (B2 C2). Or they can be repeated for emphasis or clarity. This works for determiners too.
I put on the red shirt and hat [the red shirt and the red hat].
Determiners are omitted if the noun is plural. The red shirt and the red hat all together is a plural noun.
However, in this situation:
The red shirt and the red hat.
you have a bigger NP formed from two conjuncted smaller NPs.
The smaller NPs need their determiner, because they are singular nouns, but the bigger NP does not. So you'd never do "The the red shirt and hat."
But you can't omit the first individual the, even if you can omit the determiner after the conjunction as sort of a "shortcut."
If each of the NPs were plural then you may be in a situation where no determiner is needed.
Coins and cards were all over the place, I made sure to pick them up.