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20. (本小题 10 分)解方程组 $ \begin{cases} 2x - y = 5, \\ 3x + 4y = 2. \end{cases} $
答案
$\begin{cases} x=2 \\ y=-1 \end{cases}$
解析
$\begin{cases}2x - y = 5 &①\\3x + 4y = 2 &②\end{cases}$
由①得：$y = 2x - 5$ ③
将③代入②得：$3x + 4(2x - 5) = 2$
$3x + 8x - 20 = 2$
$11x = 22$
$x = 2$
将$x = 2$代入③得：$y = 2×2 - 5 = -1$
所以方程组的解为$\begin{cases}x = 2 \\ y = -1\end{cases}$
由①得：$y = 2x - 5$ ③
将③代入②得：$3x + 4(2x - 5) = 2$
$3x + 8x - 20 = 2$
$11x = 22$
$x = 2$
将$x = 2$代入③得：$y = 2×2 - 5 = -1$
所以方程组的解为$\begin{cases}x = 2 \\ y = -1\end{cases}$
