And how would an 80 amp car alternator keep up with a 10000 watt inverter? You would need more like 800 amps.
Sunshine suggested "80amp car alternator charging 2 normal auto n70s in parallel" meaning the 80A alternator charges the two 70AH batteries. Between the alternator and the two batteries, running heavy loads won't be an issue for short peaks, and maintaining enough power for the base load.
Again, this type of inverter and usage would be to support motor startup currents. The average use should be 2-5kW so the overhead is available for motors.