[ Systems of Linear Equations ]

Solve the system of equations:

$$
\begin{aligned}
& x_{1}+x_{2}+x_{3}=6 \\
& x_{2}+x_{3}+x_{4}=9 \\
& x_{3}+x_{4}+x_{5}=3 \\
& x_{4}+x_{5}+x_{6}=-3
\end{aligned}
$$

$$
x_{5}+x_{6}+x_{7}=-9
$$

$$
x_{6}+x_{7}+x_{8}=-6,
$$

$x_{7}+x_{8}+x_{1}=-2$

$x_{8}+x_{1}+x_{2}=2$
Adding all the equations, we get $3\left(x_{1}+x_{2}+\ldots+x_{8}\right)=0$. Adding the first, fourth, and seventh equations, we get $2 x_{1}+x_{2}+x_{3}+\ldots+x_{8}=1$. Therefore, $x_{1}=1$. The other unknowns are found similarly.

## Answer

$(1,2,3,4,-4,-3,-2,-1)$.