A natural history museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Some of the money is borrowed at 5%, some at 6.5%, and some at 7.5%. Use a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $129,750 and the amount borrowed at 6.5% is four times the amount borrowed at 7.5%. Solve the system of linear equations using matrices.