6.14. (NPR, 68). Find all values of $n \in \mathbf{N}$ for which there exists a set of positive numbers $x_{1}, \ldots, x_{\mu}$, satisfying the system

$$
\left\{\begin{array}{l}
x_{1}+x_{2}+\ldots+x_{n}=9 \\
\frac{1}{x_{1}}+\frac{1}{x_{2}}+\ldots+\frac{1}{x_{n}}=1
\end{array}\right.
$$

Indicate all such sets for each of the found values of $n$.