An investor divides $10,000 of his savings into two accounts that will earn him interest. One account is a high-risk high yield account that ends up giving him an average of 12.1% interest per annum that year. The other is a safer savings account that gives him 3.1% interest per annum. If at the end of one year he has a total of $10,805 in the two accounts combined, how much did he invest at each rate? Make sure to show your work.