$a_1, a_2, a_3, a_4$가 서로 다른 네 실수일 때, 다음 연립방정식을 풀어라.
\begin{align*} & & \left| a_1-a_2 \right| x_2 &{}+{}& \left| a_1-a_3 \right| x_3 &{}+{}& \left| a_1-a_4 \right| x_4 &= 1 \\ \left| a_2-a_1 \right| x_1 & & &{}+{}& \left| a_2-a_3 \right| x_3 &{}+{}& \left| a_2-a_4 \right| x_4 &= 1 \\ \left| a_3-a_1 \right| x_1 &{}+{}& \left| a_3-a_2 \right| x_2 & & &{}+{}& \left| a_3-a_4 \right| x_4 &= 1 \\ \left| a_4-a_1 \right| x_1 &{}+{}& \left| a_4-a_2 \right| x_2 &{}+{}& \left| a_4-a_3 \right| x_3 & & &= 1 \end{align*}
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