No, you can't utilise the subscription on both computers (you won't be able to update).
However, as there are viruses that do less harm to your computer than Norton, that's probably a good thing.
Uninstall Norton from both machines and install a combination of AVG or Avast antivirus with Comodo or ZoneAlarm firewall. These are free.
If you feel you MUST have a paid for product, then Eset NOD32 is the ONLY antivirus program worth paying for, and Eset Smart Security is the ONLY combination AV/Firewall worth the money.