Filing for a dispossessory (Georgia's version of an eviction) isn't that difficult but when filing through the Clerk of Court you will be asked if you are the landlord or the landlords legal representative.
You're not since you're the tenant (and, I'm going to assume that your landlord may not be aware of this person living with you?). The problem is, this isn't YOUR house; it's your landlords. If the landlord didn't agree to this you may risk the possibility of an eviction for allowing an unauthorized person to move in with you.
So pay them to get out. And don't make the mistake in the future of trying to help ANYONE get back on their feet. Such folks are often leeches and once they've found a sucker willing to give them a place to reside (sorry to call you this) they ain't leaving easily!
Gail