回復 1# 艾瑞卡 的帖子
可用變數變換
\(\displaystyle
\begin{array}{l}
\left\{ \begin{array}{l}
a_1 x + b_1 (2y) = (5 - 3x)c_1 \\
a_2 x + b_2 (2y) = (5 - 3x)c_2 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
\displaystyle 2a_1 (\frac{x}{2}) + 3b_1 (\frac{2}{3}y) =- (-5 + 3x)c_1 \\
\displaystyle 2a_2 (\frac{x}{2}) + 3b_2 (\frac{2}{3}y) = -(-5 + 3x)c_2 \\
\end{array} \right. \\
\left\{ \begin{array}{l}
\displaystyle 2a_1 (\frac{x}{{2(-5 + 3x)}}) + 3b_1 (\frac{2}{{3(-5 + 3x)}}y) = -c_1 \\
\displaystyle 2a_2 (\frac{x}{{2(-5 + 3x)}}) + 3b_2 (\frac{2}{{3(-5 + 3x)}}y) = -c_2 \\
\end{array} \right. \\
\displaystyle \frac{x}{{2(-5 + 3x)}} = 1 \to x = 2 \\
\displaystyle \frac{2}{{3(-5 + 3x)}}y{\rm{ = }} - {\rm{2}} \to y =-3
\end{array}
\)
[ 本帖最後由 eyeready 於 2017-1-10 11:32 PM 編輯 ]