Samantha invested a total of $\$ 10,000$ in two accounts. After a year, one account lost $6.2 \%$, while the other account gained $6.1 \%$. In total, Samantha lost $\$ 374$. Write and solve a system of equations to find how much money Samantha invested in each.
Samantha invested $\square$ in the account with $6.2 \%$ loss and $\square$ in the account with $6.1 \%$ gain.

Note: Include the dollar sign (\$) in your answer. For example \$257.34

Note: You can earn partial credit on this problem.

Step 1 ：Let's denote the amount of money Samantha invested in the account with 6.2% loss as \(x\) and the amount she invested in the account with 6.1% gain as \(y\).

Step 2 ：We know that the total amount of money she invested is \$10,000, so we have the first equation: \(x + y = 10000\).

Step 3 ：After a year, the account with 6.2% loss lost 6.2% of \(x\), and the account with 6.1% gain gained 6.1% of \(y\). But in total, Samantha lost \$374. So we have the second equation: \(0.062x - 0.061y = 374\).

Step 4 ：Now we have a system of two equations with two variables. We can solve this system to find the values of \(x\) and \(y\).

Step 5 ：The solution to the system of equations is \(x = 8000\) and \(y = 2000\).

Step 6 ：\(\boxed{\text{Final Answer: Samantha invested \$8000 in the account with 6.2 \% loss and \$2000 in the account with 6.1 \% gain.}}\)