The circulatory system means to "circulate" blood that contains vital oxygen and nutrients needed by the body to function. The respiratory system works with the circulatory system in a way of the respiration. When we inhale, in the lungs containing the alveoli in which exchange of oxygen and carbon dioxide takes place. The oxygen is now joined in the blood that has entered the pulmonary artery and going back to the hear in the way of pulmonary vein, the left atrium with oxygenated blood. and now it can be distributed to all vital organs of the body.
The circulation of the blood is not complete without the respiration as it contains oxygen and that we inhale, the blood from the pulmonary artery is now oxygenated. And when we exhale, carbon dioxide is now released. (but some other biology students claim that nitrogen is released when we exhale rather than of that carbon dioxide lol)