Question

13．已知關(guān)于x，y的方程組$\left\{{\begin{array}{l}{2ax+by=14}\\{5ax-2by=8}\end{array}}\right.$的解為$\left\{{\begin{array}{l}{x=1}\\{y=2}\end{array}}\right.$，求a，b的值．

Answer 1

分析 把x與y的值代入方程組得到關(guān)于a與b的方程組，求出方程組的解即可得到a與b的值．

解答 解：把$\left\{{\begin{array}{l}{x=1}\\{y=2}\end{array}}\right.$代入方程組$\left\{{\begin{array}{l}{2ax+by=14}\\{5ax-2by=8}\end{array}}\right.$，
可得$\left\{{\begin{array}{l}{2a+2b=14}\\{5a-4b=8}\end{array}}\right.$，
解得：$\left\{{\begin{array}{l}{a=4}\\{b=3}\end{array}}\right.$．
則a=4，b=3．

點(diǎn)評(píng) 此題考查了二元一次方程組的解，方程組的解即為能使方程組中兩方程都成立的未知數(shù)的值．