Solve the system of equations:
$$
\sqrt{\bar{x}}+\sqrt{-\frac{\bar{y}}{x}}=\frac{5}{2},
$$
$$
x+y=10 \text {. }
$$
Solve (1), $\frac{x+y}{\sqrt{x y}}=\frac{5}{2}$.
(2) Substituting (3), we get $\sqrt{x y}=4$,
$$
\therefore x y=16 \text {. }
$$

From (2) and (4), we obtain the system of symmetric equations
$$
\begin{array}{l}
x+y=10 \\
x y=16
\end{array}
$$