Step 1 :Let's denote the amount invested at 9% as x and the amount invested at 12% as y.
Step 2 :We know that the total amount invested is $70,000, so we have the equation \(x + y = 70000\).
Step 3 :The total annual income from the investments was $7,200, which is the sum of the income from the two investments.
Step 4 :The income from the investment at 9% is 0.09x and the income from the investment at 12% is 0.12y. So we have the equation \(0.09x + 0.12y = 7200\).
Step 5 :We can solve this system of equations to find the values of x and y.
Step 6 :The solution is \(x = 40000\) and \(y = 30000\).
Step 7 :Final Answer: The amount invested at 9% is \(\boxed{40000}\).