[ Systems of linear equations ]

Solve the system of equations:

$$
\begin{aligned}
& x_{1}+12 x_{2}=15, \\
& x_{1}-12 x_{2}+11 x_{3}=2, \\
& x_{1}-11 x_{3}+10 x_{4}=2, \\
& x_{1}-10 x_{4}+9 x_{5}=2, \\
& x_{1}-9 x_{5}+8 x_{6}=2, \\
& x_{1}-8 x_{6}+7 x_{7}=2, \\
& x_{1}-7 x_{7}+6 x_{8}=2, \\
& x_{1}-6 x_{8}+5 x_{9}=2, \\
& x_{1}-5 x_{9}+4 x_{10}=2, \\
& x_{1}-4 x_{10}+3 x_{11}=2, \\
& x_{1}-3 x_{11}+2 x_{12}=2, \\
& x_{1}-2 x_{12}=2 .
\end{aligned}
$$
Adding the first two equations, we get $2 x_{1}+11 x_{3}=17$; adding the first three equations, we get $3 x_{1}+10 x_{4}=$ 19; ...; adding all the equations, we get $12 x_{1}=37$. From this, $x_{1}={ }^{37} / 12, x_{2}=\left(15-x_{1}\right): 12=143 / 144, x_{3}=\left(17-2 x_{1}\right)$ $: 11=65 / 66$, and so on.

## Answer

$\left({ }^{37} / 12,{ }^{143} / 144,{ }_{6}^{65} / 66,{ }^{39} / 40,{ }^{26 / 27},{ }^{91 / 96},{ }^{13} / 14,{ }^{65} / 72,{ }^{13} / 15,{ }^{13} / 16,{ }^{13} / 18,{ }^{13} / 24\right)$.