Andre wants to purchase some onions and tomatoes to make tomato soup for a large event. He looks at two different recipes. One of the recipes for tomato soup states that 4 times the number of tomatoes, x, plus 5 times the number of onions, y, should produce 109 bowls of tomato soup. The other recipe for tomato soup states that 2 times the number of tomatoes used minus the number of onions used should produce 23 bowls of tomato soup.

Create a system of equations representing the two recipes. How many tomatoes and onions will Andre need to purchase to satisfy both recipes?