What was the name of the trade system that interacted with the West Indies, the Americans, and Europe

The Colombian exchange is your answer.

These two-way exchanges between the Americas and Europe/Africa are known collectively as the Columbian Exchange. Of all the commodities in the Atlantic World, sugar proved to be the most important. Indeed, in the colonial era, sugar carried the same economic importance as oil does today.

https://www.khanacademy.org/humanities/us-history/precontact-and-early-colonial-era/old-and-new-worlds-collide/a/the-columbian-exchange-ka