Purchased a PS3 with games already on it

Solution 1:

Games and DLC downloaded on one user profile (with its PSN user) on the system can (usually) be accessed by other profiles and PSN users on the same system. As long as a system is "activated" for an account, it can play games bought by it. This means you can create your own profile on the system with a new PSN account and still access the original owner's games.

Each PSN account can be activated on up to two PS3 systems and two portables systems (Vita/PSP). The original owner can choose to deactivate your system remotely, and this will stop the games from working on your system (this applies if your system is connected to the internet, since the system checks if the console is activated fro an account periodically when your start running a game). I'd say you're safe to play his games on your account, be don't rely on them being available forever. In any case, avoid logging into his account if he kept the password stored on the system, since this will log him out if he's currently logged in and vice versa.