Solve the following system of equations:

$$
\frac{4}{\sqrt{x+5}}-\frac{3}{\sqrt{y+2}}=1, \quad \frac{2}{\sqrt{x+5}}+\frac{9}{\sqrt{y+2}}=4 .
$$
By replacing the first term of the second equation with $z$ and the subtrahend of the first equation with $w$, we obtain the following system of equations for the new unknowns:

$$
2 z-w=1, \quad z+3 w=4, \quad \text{and from this} \quad z=w=1
$$

Thus, for $x$ and $y$, from the single-variable equations

$$
\frac{2}{\sqrt{x+5}}=1, \quad \frac{3}{\sqrt{y+2}}=1
$$

we get $x=-1, y=7$.

Borossay Béla (Szombathely, Nagy Lajos. g. II. o. t.)