The body system that allows a person to walk, talk, and breathe is the respiratory system. The respiratory system is composed of the airway, the lungs, and the muscles of the respiration. The respiratory system allows a person to taken in the air allowing him to breathe in the oxygen, and breathe out the carbon-dioxide. The ability to speak is also dependent on the breathing in of the air. The person can walk, or run, as a thanks to his respiratory system, which is constantly inhaling oxygen to provide him the energy.
Hence, the answer is 'respiratory system'.