Question

17．方程mx+ny=10的两组解是$\left\{\begin{array}{l}{x=-1}\\{y=2}\end{array}\right.$和$\left\{\begin{array}{l}{x=1}\\{y=3}\end{array}\right.$，求m和n的值．

Answer 1

分析 把x与y的两对值代入方程计算即可求出m与n的值．

解答 解：把$\left\{\begin{array}{l}{x=-1}\\{y=2}\end{array}\right.$和$\left\{\begin{array}{l}{x=1}\\{y=3}\end{array}\right.$代入方程得：$\left\{\begin{array}{l}{-m+2n=10}\\{m+3n=10}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{m=-2}\\{n=4}\end{array}\right.$．

点评 此题考查了二元一次方程的解，方程的解即为能使方程左右两边相等的未知数的值．