Question

what systems are most responsible for providing cells with oxygen and removing the carbon dioxide?

Answer 1

Assuming it's about the human body, it can be looked at from the point of view of what's bringing in the needed materials. Assuming aerobic catabolism is at issue, then one body system must bring in the fuel, and another the oxygen; those would be the digestive and respiratory systems, respectively. If a narrow enough view of "providing" is taken, then the circulatory system can be left out of consideration, since once the stuff is in the body, it may be considered to be "provided for cells". Of course that's like buying goods without delivery, but if you insist on only 2 systems as responsible, that's what you've got.