Your mother's debts should be paid with the property in her estate -- that is, the property she left at her death. You have not inherited these debts.

However, the debts do affect you to the extent that they will have to be paid before any inheritance is handed out. Also, if you inherit property that is collateral for a debt -- for example, a car that is not paid for, or a house with a mortgage -- the debt comes with the property.