Question

16．若$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$和$\left\{\begin{array}{l}{x=3}\\{y=-5}\end{array}\right.$都是方程ax+by+2=0的解，试判断$\left\{\begin{array}{l}{x=-4}\\{y=9}\end{array}\right.$是否为方程ax+by+2=0的一个解？

Answer 1

分析 先把$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$和$\left\{\begin{array}{l}{x=3}\\{y=-5}\end{array}\right.$都代入方程ax+by+2=0，求出a，b的值，再求出方程的式子，把$\left\{\begin{array}{l}{x=-4}\\{y=9}\end{array}\right.$代入判定是否为方程的一个解即可．

解答 解：把$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$和$\left\{\begin{array}{l}{x=3}\\{y=-5}\end{array}\right.$都代入方程ax+by+2=0，得：
$\left\{\begin{array}{l}{a-b+2=0}\\{3a-5b+2=0}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=-4}\\{b=-2}\end{array}\right.$，
所以方程为-4x-2y+2=0，
把$\left\{\begin{array}{l}{x=-4}\\{y=9}\end{array}\right.$代入得左边=0=右边，
则$\left\{\begin{array}{l}{x=-4}\\{y=9}\end{array}\right.$是为方程ax+by+2=0的一个解．

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a，b的值．