Question

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

Answer 1

分析 首先解兩個不等式中只含有x和y的方程組成的方程組：$\left\{\begin{array}{l}{9y=2x+1}\\{x-18y+14=0}\end{array}\right.$，求得x和y的值，然后把x和y的值代入$\left\{\begin{array}{l}{ax+by=9}\\{2ax-3y=13}\end{array}\right.$得到一個關(guān)于a和b的方程組求得a和b的值．

解答 解：根據(jù)題意得：$\left\{\begin{array}{l}{9y=2x+1}\\{x-18y+14=0}\end{array}\right.$，
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：$\left\{\begin{array}{l}{a=2}\\{b=1}\end{array}\right.$．

點評 本題考查了二元一次方程組的解的定義，了解方程組的解的定義求得x和y的值是關(guān)鍵．