The three systems interrelate for a complete function of the body. The respiratory and cardiovascular systems work together to perform the gas exchange function. Without gas exchange function, the cells would die, hence, it is crucial for these systems to work together.
Through respiratory system, the oxygen enters the body and then it is transported as oxyhaemoglobin to the cells with the help of cardiovascular system. The cardiovascular system also performs the work to transport the waste product carbon dioxide to respiratory system, that evacuates it.
Hence, whithout respiratory system, the oxygen could not enter the body and it could not discharge the carbon dioxide waste. Without cardiovascular system, the oxygen and carbon dioxide could not travel the body.
The cardiovascular system relates with digestive system for an optimum heart rate. The digestive system produces nutrients and with help of cardiovascular system transports these nutrients where it is needed. The digestive toxins are also discharged from system with the help of cardiovascular system that transports them to kidneys.
Hence, the healthy equilibrium of human body is reached if all these systems work together in harmony.
One simple aspect is as follows:
Digestive system breaks down large molecules (e.g starch) into simple molecules such as glucose. These are then transported to cells of the body via the circulatory system.
The respiratory system causes the diffusion of oxygen into the blood and the diffusion of CO2 out of the blood. This oxygen is then transported to cells of the body via the circulatory system.
When the cells have both oxygen and glucose they can respire to release energy, producing water and carbon dioxide (the CO2 is carried through the circulatory system to the lungs where it is removed through the respiratory system.