Your digestive and respiratory systems, at first glance, seem very separate in their activities. In reality, however, the systems work together intimately in several ways. The results of respiratory activity allow the digestive tract to function, and vice versa. Furthermore, the systems work together to provide energy to body cells.
The purpose of your digestive system is to take in food from your environment and break it down on both macroscopic and molecular levels. Through the process of digestion, you break large nutrient molecules into smaller ones that your intestine absorbs into the bloodstream. Cells then take up these nutrient molecules and use them to build new molecules and provide for their cellular energy needs. Cells can also store the molecules for later use.
Your respiratory system takes in oxygen from the atmosphere and moves that oxygen into the bloodstream by allowing it to move across the membranes of the lungs into the blood vessels. The circulatory system then carries oxygen to all the cells in the body and picks up carbon dioxide waste, which it returns to the lungs. Carbon dioxide diffuses from the blood into the lungs, and you exhale it into the atmosphere.
Digestive Dependence Upon Respiration
The digestive tract is dependent upon the respiratory system, because your digestive tract functions by using muscular contractions to break up food and move it along the tract. Smooth muscle in the stomach churns food into a liquid, and contractions of the intestine move food through the system. These muscles depend upon oxygen in order to function -- without oxygen, your digestive tract would stop working.
Respiratory Dependence Upon Digestion
Similarly, your respiratory tract wouldn't be able to function without the products of digestion. While the process of exhalation is passive and doesn't require muscular contraction, you contract the respiratory muscles -- including the diaphragm and intercostal muscles -- to inhale. Muscles need fuel in order to contract, and the fuel they use is primarily in the form of carbohydrate and fat. The efforts of the digestive tract provide the cells of the respiratory muscles with fuel.
Cellular Dependence Upon Both Systems
The body cells depend upon products of both the respiratory and digestive systems' functions in order to maintain themselves. To produce energy, cells burn nutrient molecule fuel in oxygen. The digestive tract provides the nutrient molecules, through the process of digestion, while the respiratory tract provides oxygen. As such, the two systems work together to give your cells the ingredients they need to produce energy, which they use to communicate, build cellular products and grow.