Question

11．若方程组$\left\{\begin{array}{l}{x+2y=4}\\{x-2y=0}\end{array}\right.$与方程组$\left\{\begin{array}{l}{x-my=-2}\\{nx-y=3}\end{array}\right.$的解相同，则m+n的值为6．

Answer 1

分析 解方程组$\left\{\begin{array}{l}{x+2y=4}\\{x-2y=0}\end{array}\right.$求得x、y的值，代入方程组$\left\{\begin{array}{l}{x-my=-2}\\{nx-y=3}\end{array}\right.$求解得m、n的值，即知m+n．

解答 解：解方程组$\left\{\begin{array}{l}{x+2y=4}\\{x-2y=0}\end{array}\right.$，得：$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，
将$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{x-my=-2}\\{nx-y=3}\end{array}\right.$得：$\left\{\begin{array}{l}{2-m=-2}\\{2n-1=3}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{m=4}\\{n=2}\end{array}\right.$，
∴m+n=6，
故答案为：6．

点评 本题主要考查解二元一次方程组和二元一次方程组的解，熟练掌握解方程组的技能和方程组的解的定义是解题关键．