Question

4．若$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=-1}\end{array}\right.$是方程mx+ny=6的兩個解，則mn=-4．

Answer 1

分析 把x與y的兩對值代入方程計算求出m與n的值，即可確定出mn的值．

解答 解：把$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=-1}\end{array}\right.$代入方程得：$\left\{\begin{array}{l}{4m+n=6①}\\{2m-n=6②}\end{array}\right.$，
①+②得：6m=12，即m=2，
把m=2代入②得：n=-2，
則mn=-4，
故答案為：-4

點評 此題考查了二元一次方程的解，方程的解即為能使方程左右兩邊相等的未知數(shù)的值．