The Circulatory system pumps blood around the body, and the respiratory system facilitates the gas exchange that keeps the blood fresh. The heart is connected to the lungs via the pulmonary arteries and veins. The circulatory and respiratory systems work together to deliver oxygen and other important nutrients to every cell in our bodies. All of our body cell require oxygen to conduct cellular respiration. In this process, oxygen burns the nutrients from foods w eat, providing energy for the cells.