KöMaL 2020 B5121

Solve the following simultaneous equations, where $x_1, x_2,\ldots,x_n$ are positive real numbers, and $n$ is a positive integer: $$\begin{align*} x_1+x_2+\ldots +x_n & =9,\\ \frac1{x_1}+\frac1{x_2}+\ldots +\frac1{x_n} & =1. \end{align*}$$