3.18. Answer: $x_{1}=-x_{8}=1, x_{2}=-x_{7}=2, x_{3}=-x_{6}=3, x_{4}=$ $=-x_{5}=4$.

By adding all the equations, we get $3\left(x_{1}+x_{2}+\ldots+x_{8}\right)=0$. Then, by adding the first, fourth, and seventh equations, we obtain $2 x_{1}+x_{2}+x_{3}+\ldots+x_{8}=1$, which means $x_{1}=1$. The other unknowns are found similarly.
3.18. Solve the system of equations

$$
\left\{\begin{array}{l}
x_{1}+x_{2}+x_{3}=6 \\
x_{2}+x_{3}+x_{4}=9 \\
x_{3}+x_{4}+x_{5}=3 \\
x_{4}+x_{5}+x_{6}=-3 \\
x_{5}+x_{6}+x_{7}=-9 \\
x_{6}+x_{7}+x_{8}=-6 \\
x_{7}+x_{8}+x_{1}=-2 \\
x_{8}+x_{1}+x_{2}=2
\end{array}\right.
$$