How did the inca empire manage to function without a system of writing?

The Inca had absolutely no form of writing whatsoever. So they didn't know how to write anything. This was a problem so they had to invent other ways to kind of keep track of records and other important things.

As a result, the Aztecs used quipu.

Quipu was a mathematical system and it was commonly used throughout the Inca empire to record and transmit data. So, the fact that they were able to get around this huge barrier is pretty amazing.