Mardi received an inheritance of $\$ 70,000$. She invested part at $9 \%$ and deposited the remainder in tax-free bonds at $12 \%$. Her total annual income from the investments was $\$ 7,200$. Find the amount invested at $9 \%$.

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 \(\boxed{40000}\).