Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.
Wendy likes to make desserts for bake sales. Last month, she made 1 batch of cookies, which called for 2 eggs total. The month before, she baked 3 batches of brownies and 1 batch of cookies, which required a total of 11 eggs. How many eggs did Wendy use for a batch of each dessert?
Wendy uses___ eggs to make a batch of brownies and _____ eggs to make a batch of cookies.