Question

9．若$\left\{\begin{array}{l}{x=1}\\{y=-2}\end{array}\right.$是方程组$\left\{\begin{array}{l}{mx+ny=7}\\{mx-ny=-1}\end{array}\right.$的解，则m=3，n=-2．

Answer 1

分析 将$\left\{\begin{array}{l}{x=1}\\{y=-2}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{mx+ny=7}\\{mx-ny=-1}\end{array}\right.$可得关于m、n的方程组，解之可得．

解答 解：根据题意，将$\left\{\begin{array}{l}{x=1}\\{y=-2}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{mx+ny=7}\\{mx-ny=-1}\end{array}\right.$，
得：$\left\{\begin{array}{l}{m-2n=7}\\{m+2n=-1}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{m=3}\\{n=-2}\end{array}\right.$，
故答案为：3，-2．

点评 本题主要考查方程组的解得概念和解方程组的能力，根据题意得出关于m、n的方程组是解题的关键．