How does the system know that the ticket was already used?

The thing with plane and long-distance train tickets is that you buy them for a specific route. So all the checking only needs to be done at your departure station/airport, the code for which is encoded in the ticket, and the rest of the system doesn't need to know anything about it. But you can't do that with city transport. When there aren't multi-use tickets, people would often buy multiple single-use ones at a time and use them as the need arises, without knowing in advance when, where, and from where they'll be going.