What did farmers in the Inca empire do to grow food?

The Inca carved terraces around the hills to use the farmland they had and conserve space. This allowed them to farm on hills.

Answer

Farming on terraces is advantageous because it allows for a longer growing season, since it changes airflow, cooling in hot seasons and reducing the loss of ground temperature in the winter. Also, more of the water flowing down from snow or rain is captured, and erosion is tempered.