Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Anita likes to make desserts for bake sales. Last month, she made 1 batch of brownies and 1 batch of cookies, which called for 5 eggs total. The month before, she baked 3 batches of brownies and 1 batch of cookies, which required a total of 9 eggs. How many eggs did Anita use for a batch of each dessert?

Anita uses
eggs to make a batch of brownies and
eggs to make a batch of cookies.