You would use the digestive system (which includes your mouth and teeth) to chew, swallow, and begin digesting the carrot. You would use the nervous system to taste and smell the carrot. You would use the muscular system to close and open your jaw to chew the carrot and also to raise the carrot to your mouth and to maintain posture. You would also use the muscular system to swallow and digest the food using peristalsis (which is the back and forth motion by smooth muscle to churn the carrot). You would use the skeletal system (specifically the maxillae (upper jaw and hard palate) and the mandible (lower jaw)) as support for your muscles to chew the carrot and the skeletal system to maintain posture while sitting at the table. These are the systems directly involved with ingesting a carrot.