Scott invested a total of $\$ 5900$ at two separate banks. One bank pays simple interest of $11 \%$ per year while the other pays simple interest at a rate of $9 \%$ per year. If Scott earned $\$ 593.00$ in interest during a single year, how much did he have on deposit in each bank?

Scott had $\$ \square$ on deposit at the bank that payed $11 \%$ interest.
Scott had $\$ \square$ on deposit at the bank that payed $9 \%$ interest.

Step 1 ：Let's denote the amount of money Scott deposited in the bank that pays 11% interest as \(x\) and the amount he deposited in the bank that pays 9% interest as \(y\).

Step 2 ：From the problem, we know that the total amount of money Scott deposited is $5900. So we can write the first equation as \(x + y = 5900\).

Step 3 ：We also know that Scott earned $593 in interest in a year. The interest from the first bank is \(0.11x\) and from the second bank is \(0.09y\). So we can write the second equation as \(0.11x + 0.09y = 593\).

Step 4 ：We can solve the first equation for \(x\), which gives us \(x = 5900 - y\).

Step 5 ：Substitute \(x = 5900 - y\) into the second equation, we get \(0.11(5900 - y) + 0.09y = 593\), which simplifies to \(649 - 0.02y = 593\).

Step 6 ：Solving this equation for \(y\), we get \(y = 2800\).

Step 7 ：Substitute \(y = 2800\) back into the first equation, we get \(x = 5900 - 2800 = 3100\).

Step 8 ：So, Scott had \(\boxed{3100}\) dollars on deposit at the bank that payed 11% interest and \(\boxed{2800}\) dollars on deposit at the bank that payed 9% interest.