The job of the respiratory system is to supply cells with oxygen for cell respiration. However, that is not all the cells need for cell respiration. They cells also need glucose. That glucose "made" by the digestive system, this systems specific job.The glucose and oxygen are taken through the respiratory system and are given to cells. The cells then use the substances given to them to make energy, a vital substance to the body. The two systems work together to complete cellular respiration which benefits the whole body. This shows how the digestive system and the respiratory work together to supply those two substances to cells, something each system is made out of.
small_intestine.gif
In the picture to the right, you can see where the small intestine is. The is where the food is broken into glucose and the small intestine also has capillaries. The capillaries allow the glucose to be absorbed and sent to the cells.

For more information about the digestive system- http://digestive.niddk.nih.gov/ddiseases/pubs/yrdd/