3.19. Let $a, b, c$ be pairwise distinct numbers. Solve the system of equations

$$
\left\{\begin{array}{l}
x + a y + a^{2} z + a^{3} = 0 \\
x + b y + b^{2} z + b^{3} = 0 \\
x + c y + c^{2} z + c^{3} = 0
\end{array}\right.
$$

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3.19. Consider the polynomial $P(t)=t^{3}+t^{2} z+t y+x$. The pairwise distinct numbers $a, b, c$ are roots of the polynomial $P(t)$. Therefore, $P(t)=(t-a)(t-b)(t-c)$, which means $x=-a b c, y=a b+b c+c a$, $z=-(a+b+c)$.