How can you connect a system working with 60Hz 1 Hot wire 1 neutral wire and a ground wire to my utility system that works with 60Hz two hot wires and a neutral wire?

Your 2-wire system is actually connected to one "side" of the 3-wire system.

In your utility's 3-wire system you have 2 hot wires that are attached to each end of a tranformer winding and the neutral is attached in the middle and grounded. Typically in the US this gives you 240v (or something similar) between hot leads and 120v from each hot lead to neutral or ground.