How do the respiratory and circulatory systems work together to get oxygen into your cells?

The respiratory system allows the entry of air with oxygen, which diffuses at the level of the alveolus-capillary barrier to the blood, and the circulatory system transports the oxygenated blood to cell of all tissues.

Explanation:

The bioavailability of oxygen (O₂) in each cell of the body depends on the joint function of the respiratory and circulatory systems, which work together for this purpose.

The respiratory system allows air, which contains O₂, to enter the lungs, leading it to the pulmonary alveoli.
At the alveolar level there is a gas exchange barrier, the alveolus-capillary barrier, through which O₂ passes into the blood, while carbon dioxide from cellular maetabolism passes into the alveolus to be eliminated.
Once O₂ is in the blood, it is transported through the circulatory system to all tissues, being used by the cells for the process of cellular respiration and energy metabolism.

Pulmonary respiration is a process that, in coordination between the respiratory and circulatory systems, allows cellular respiration.