Question 5
(CZS) Solve the following system of equations:
$$\begin{aligned}|a_1-a_2|x_2+|a_1-a_3|x_3+|a_1-a_4|x_4&=1,\\|a_2-a_1|x_1+|a_2-a_3|x_3+|a_2-a_4|x_4&=1,\\|a_3-a_1|x_1+|a_3-a_2|x_2+|a_3-a_4|x_4&=1,\\|a_4-a_1|x_1+|a_4-a_2|x_2+|a_4-a_3|x_3&=1,\end{aligned}$$
where $a_1,a_2,a_3,a_4$ are mutually distinct real numbers.
$$\begin{aligned}|a_1-a_2|x_2+|a_1-a_3|x_3+|a_1-a_4|x_4&=1,\\|a_2-a_1|x_1+|a_2-a_3|x_3+|a_2-a_4|x_4&=1,\\|a_3-a_1|x_1+|a_3-a_2|x_2+|a_3-a_4|x_4&=1,\\|a_4-a_1|x_1+|a_4-a_2|x_2+|a_4-a_3|x_3&=1,\end{aligned}$$
where $a_1,a_2,a_3,a_4$ are mutually distinct real numbers.