Question

8．若方程組$\left\{\begin{array}{l}{5mx-6ny=2}\\{nx+my=8}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，求m．n的值．

Answer 1

分析 直接把$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入$\left\{\begin{array}{l}{5mx-6ny=2}\\{nx+my=8}\end{array}\right.$可得關(guān)于m、n的方程組，再解方程組即可．

解答 解：把$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入$\left\{\begin{array}{l}{5mx-6ny=2}\\{nx+my=8}\end{array}\right.$得$\left\{\begin{array}{l}{10m-6n=2}\\{2n+m=8}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{m=2}\\{n=3}\end{array}\right.$．

點(diǎn)評(píng) 此題主要考查了二元一次方程組的解，當(dāng)遇到有關(guān)二元一次方程組的解的問(wèn)題時(shí)，要回到定義中去，通常采用代入法，即將解代入原方程組，這種方法主要用在求方程中的字母系數(shù)．