Question

6．已知方程组$\left\{\begin{array}{l}{x+y=n}\\{x=3}\end{array}\right.$和$\left\{\begin{array}{l}{3x+y=8}\\{x+2y=m}\end{array}\right.$有相同的解，求m与n的值．

Answer 1

分析 根据方程组$\left\{\begin{array}{l}{x+y=n}\\{x=3}\end{array}\right.$和$\left\{\begin{array}{l}{3x+y=8}\\{x+2y=m}\end{array}\right.$有相同的解，可知两个方程组的解适合方程组中的每个方程，从而可得方程组$\left\{\begin{array}{l}{x=3}\\{3x+y=8}\end{array}\right.$的解，然后代入$\left\{\begin{array}{l}{x+y=n}\\{x+2y=m}\end{array}\right.$即可得到m、n的值，本题得以解决．

解答 解：∵方程组$\left\{\begin{array}{l}{x+y=n}\\{x=3}\end{array}\right.$和$\left\{\begin{array}{l}{3x+y=8}\\{x+2y=m}\end{array}\right.$有相同的解，
∴$\left\{\begin{array}{l}{x=3}\\{3x+y=8}\end{array}\right.$，
解得，$\left\{\begin{array}{l}{x=3}\\{y=-1}\end{array}\right.$
将$\left\{\begin{array}{l}{x=3}\\{y=-1}\end{array}\right.$代入$\left\{\begin{array}{l}{x+y=n}\\{x+2y=m}\end{array}\right.$，得$\left\{\begin{array}{l}{m=1}\\{n=2}\end{array}\right.$，
即m的值是1，n的值是2．

点评 本题考查二元一次方程组的解，解题关键是明确如果两个方程组的解相同，则这组解适合两个方程组中的任何一个方程．