It is very unusual to use coax cable as speaker wire. Coax is usually run to an electronics gadget of some sort that may be connected to a speaker. Have you verified that there is one wire per speaker at the central location? Have you verified that coaxial wire is connected to each speaker? Are there any signs of electronics scattered about that could operate speakers? There could be remote Volume controls or some sort of keypad in each room. What kind of connections are used at the end of each coax at the central location?
At this point we cannot assume that this is or was a competent installation. There are a lot of weird ideas out there. If the system was a few decades old, its design will be very different when compared with more modern approaches. Decades ago multi-room systems were on the edge and required some imagination to implement.
Consider the possibility that the coax is connected to cable jacks, not speakers. If this is the case, there will be speaker wires or jacks scattered about.
As a crude test, connect a flashlight cell to one of the central coax cables. If the other end is connected to a speaker, there will be a “thump” from the speaker at the instant of connection. Connect one end of the battery to the inner coax wire and the other end of the battery to the outer metal shield. You’ll need an assistant to perform this test. If you get a “thump”, label the wire and continue with the others.
Consider calling in an expert friend or hiring a pro to sort things out. Take care when selecting that “expert” friend. Many self declared experts are actually hazards.