36.2. Solve the system of equations:

$$
\left\{\begin{array}{l}
\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1 \\
a x=b y=c z
\end{array}\right.
$$

$(8-9$ grades)

$\left\{\begin{array}{l}\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1, \\ a x=b y=c z .\end{array}\right.$
36.2. Since none of the numbers $x, y, z$ can be equal to 0, multiplying all terms of the first equation by $x$, we get:

$$
1+\frac{x}{y}+\frac{x}{z}=x
$$

At the same time, from the second equation we have: $\frac{x}{y}=\frac{b}{a}, \frac{x}{z}=\frac{c}{a}$. Then $x=1+\frac{b}{a}+\frac{c}{a}=\frac{a+b+c}{a}$. Similarly, we obtain:

$$
y=\frac{a+b+c}{b}, \quad z=\frac{a+b+c}{c}
$$