A state government borrows $2,000,000 at simple annual interest. 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 (in dollars) is borrowed at each rate given that the total annual interest is $121,250 and the amount borrowed at 6.5% is four times the amount borrowed at 7.5%. Solve the system of linear equations using matrices.
