Question

12．關于x、y的二元一次方程組$\left\{\begin{array}{l}{mx+ny=8}\\{2mx-3ny=-4}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=2}\\{y=4}\end{array}\right.$，求m+n的值．

Answer 1

分析 把$\left\{\begin{array}{l}{x=2}\\{y=4}\end{array}\right.$代入方程組得出$\left\{\begin{array}{l}{2m+4n=8①}\\{4m-12n=-4②}\end{array}\right.$，①×2得出4m+8n=16③，②-③即可求出n=1，把n=1代入②求出m，即可得出答案．

解答 解：把$\left\{\begin{array}{l}{x=2}\\{y=4}\end{array}\right.$代入方程組得：$\left\{\begin{array}{l}{2m+4n=8①}\\{4m-12n=-4②}\end{array}\right.$，
①×2得：4m+8n=16③，
②-③得：n=1，
把n=1代入②得：m=2，
所以m+n=3．

點評 本題考查了二元一次方程組的解，解二元一次方程組的應用，能得出m、n的值是解此題的關鍵．