Final answer:
The passage of arterial blood carrying oxygen to the body's organs and exchanging it for carbon dioxide falls within the function of the Circulatory System, specifically through the systemic and pulmonary circulations.
Step-by-step explanation:
The passage of arterial blood from the heart's left atrium towards the left ventricle, to the arteries and then to the capillaries, to the organs and tissues in exchange for carbon dioxide is pathway of the Circulatory System. The systemic circulation is the part of the cardiovascular system that carries oxygen-rich blood away from the heart to the body and returns oxygen-poor blood back to the heart. The organs and tissues use the oxygen for vital functions and then the blood, now holding carbon dioxide, returns to the heart. This deoxygenated blood is then sent to the lungs via the pulmonary circulation, where the carbon dioxide is exchanged for fresh oxygen.
The respiratory system is closely related as it handles the exchange of gases between the body and the outside air, including the uptake of oxygen and exhalation of carbon dioxide. However, the actual circulation of blood throughout the body is the primary function of the circulatory system.