Alimentary is a word connected with our alimentary canal. It means ‘connected with food, nutrition’. For example: “The surgeon removed an obstruction in Hitesh’s alimentary canal.”
Elementary, on the other hand, means ‘connected with rudiments, fundamentals’. For example: “Kids are required to start elementary school at the age of 3.”
Usage example that uses these 2 words: It was at elementary school that I learned first about the fact that we have an alimentary canal.