Gary won $70,000 in the lottery after all tax deductions. he invested part of the money at 11% and deposited the remainder in tax-free bonds at 12%. his total annual income from the investments was $7900. find the amount invested at 11%. find the amount invested at 12%.

Let x represent the amount of money he invested at 11% and y money he invested at 12%. Now we write system of equations:

x*1.11 + y*1.12 = 70 000 + 7900
x + y = 70 000

We will multiply second equation with 1.11
x*1.11 + y*1.11 = 77700
and subtract if from first:
0.01*y =  200
y = 20000

x = 70000 - 20000 = 50000