Question

7．解方程组$\left\{\begin{array}{l}{|x+5|+y=4x-1}\\{|2x-4|+|y-4|=3x}\end{array}\right.$．

Answer 1

分析 根据绝对值的性质，可化简方程组，根据解方程组，可得答案．

解答 解：当x＜-5，y＜4时，$\left\{\begin{array}{l}{-x-5+y=4x-1}\\{-2x+4-y+4=3x}\end{array}\right.$，$\left\{\begin{array}{l}{x=\frac{7}{5}}\\{y=11}\end{array}\right.$不符合题意舍；
当x＜-5，y≥4时，$\left\{\begin{array}{l}{-x-5+y=4x-1}\\{-2x+4+y-4=3x}\end{array}\right.$方程组无解，
当-5≤x＜2，y＜4时，$\left\{\begin{array}{l}{x+5+y=4x-1}\\{-2x+4-y+4=3x}\end{array}\right.$解得$\left\{\begin{array}{l}{x=\frac{7}{4}}\\{y=-\frac{3}{4}}\end{array}\right.$；
当-5≤x＜2，y≥4时，$\left\{\begin{array}{l}{x+5+y=4x-1}\\{-2x+4+y-4=3x}\end{array}\right.$解得$\left\{\begin{array}{l}{x=-\frac{3}{2}}\\{y=-\frac{23}{2}}\end{array}\right.$不符合题意舍；
当x≥2，y＜4时，$\left\{\begin{array}{l}{x+5+y=4x-1}\\{2x-4-y+4=3x}\end{array}\right.$，解得$\left\{\begin{array}{l}{x=\frac{3}{2}}\\{y=-\frac{3}{2}}\end{array}\right.$不符合题意舍；
当x≥2，y≥4时，$\left\{\begin{array}{l}{x+5+y=4x-1}\\{2x-4+y-4=3x}\end{array}\right.$，解得$\left\{\begin{array}{l}{x=7}\\{y=15}\end{array}\right.$，
原方程组的解为$\left\{\begin{array}{l}{x=\frac{7}{4}}\\{y=-\frac{3}{4}}\end{array}\right.$，$\left\{\begin{array}{l}{x=7}\\{y=15}\end{array}\right.$．

点评 本题考查了解二元一次方程组，分类讨论是解题关键，以防遗漏．