The products of the digestive system are actually tied directly to the circulatory system in that the organs of the digestive system are used to turn ingested food into products that can be absorbed by the blood and then carried to other organs for use as energy or other functions.
There are also several links between the digestive system and the respiratory system in that there are organs and muscles that serve both, for example the diaphragm which works to force air into and out of the lungs as well as to force waste products out of the digestive system.
All of the systems have to work together as well, without the intake of oxygen and exhalation of carbon dioxide, the function of the digestive system would grind to a halt. Without the production of glycogen and other things necessary for muscular function, produced by the digestive system and then distributed by the circulatory system, all three functions would cease.
Absorption of nutrients mainly occur in duodenum, jejunum and ileum of small intestine. The inner walls of small intestine are covered with finger like structures called villi. Each villi is covered with microvilli that protrude from absorptive cells. When digested food enters the small intestine, capillaries inside each villus allow for absorption of most nutrient into the blood by use of passive diffusion, facilitated diffusion, active transport and phagocytosis. This nutrient rich blood will be sent to the body parts through heart.
As air enters to the nose and mouth, it travels to the larynx, into the trachea, bronchial tubes, bronchioles and alveoli. The alveoli is surrounded by capillary networks and gaseous exchange will occur by taking advantage of thin alveoli and red blood cells wall. The oxygen is absorbed by hemoglobin molecules and will be sent to the heart. On the other hand the deoxygenated blood will be carried from heart to the lung capillaries and released into the alveoli then being exhaled