Question

4．已知$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$是方程组$\left\{\begin{array}{l}{mx+ny=5}\\{nx+my=1}\end{array}\right.$的解，则m-n的值是（　　）

• A． -1
• B． 2
• C． 3
• D． 4

Answer 1

分析 将$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{mx+ny=5}\\{nx+my=1}\end{array}\right.$，求出m，n的值，即可解答．

解答 解：将$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{mx+ny=5}\\{nx+my=1}\end{array}\right.$，得：$\left\{\begin{array}{l}{2m+n=5}\\{2n+m=1}\end{array}\right.$
解得：$\left\{\begin{array}{l}{m=3}\\{n=-1}\end{array}\right.$
m-n=3-（-1）=4，
故选：D．

点评 本题主要考查了二元一次方程组的解，解题的关键是求出m，n的值．