Question

13．已知二元一次方程组$\left\{\begin{array}{l}{9y=2x+1}\\{ax+by=9}\end{array}\right.$的解也是二元一次方程组$\left\{\begin{array}{l}{x-18y+14=0}\\{2ax-3y=13}\end{array}\right.$的解，求a，b的值．

Answer 1

分析 首先解两个不等式中只含有x和y的方程组成的方程组：$\left\{\begin{array}{l}{9y=2x+1}\\{x-18y+14=0}\end{array}\right.$，求得x和y的值，然后把x和y的值代入$\left\{\begin{array}{l}{ax+by=9}\\{2ax-3y=13}\end{array}\right.$得到一个关于a和b的方程组求得a和b的值．

解答 解：根据题意得：$\left\{\begin{array}{l}{9y=2x+1}\\{x-18y+14=0}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$代入$\left\{\begin{array}{l}{ax+by=9}\\{2ax-3y=13}\end{array}\right.$得：
$\left\{\begin{array}{l}{4a+b=9}\\{8a-3=13}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=2}\\{b=1}\end{array}\right.$．

点评 本题考查了二元一次方程组的解的定义，了解方程组的解的定义求得x和y的值是关键．