Question

12．方程组$\left\{\begin{array}{l}{x+2y=5}\\{x-y=8}\end{array}\right.$的解也是方程3mx+2my=57的解，求m的值．

Answer 1

分析 先解方程组$\left\{\begin{array}{l}{x+2y=5}\\{x-y=8}\end{array}\right.$得$\left\{\begin{array}{l}{x=7}\\{y=-1}\end{array}\right.$，然后把$\left\{\begin{array}{l}{x=7}\\{y=-1}\end{array}\right.$代入方程3mx+2my=57得21m-2m=57，再解关于m的一次方程即可．

解答 解：解方程组$\left\{\begin{array}{l}{x+2y=5}\\{x-y=8}\end{array}\right.$得$\left\{\begin{array}{l}{x=7}\\{y=-1}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=7}\\{y=-1}\end{array}\right.$代入方程3mx+2my=57得21m-2m=57，解得m=3．

点评 本题考查了二元一次方程组的解：二元一次方程组的两个方程的公共解，叫做二元一次方程组的解．