Which system is responsible for moving body parts as well as aiding digestion and circulation of blood by contracting and relaxing?

Answer: circulatory system

Explanation:

The digestive system operates very closely with the circulatory system for delivery of the ingested nutrients through the body. The circulatory system carries also chemical signals from the endocrine system that regulate digestion speed.

The circulatory system works closely with skeletal muscle as well to provide efficient oxygen and nutrient transfer necessary for contraction and inhibitory waste products removal.

Hence, the correct option is circulatory system.