Question

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

Answer 1

分析 根據(jù)方程組$\left\{\begin{array}{l}{x+y=n}\\{x=3}\end{array}\right.$和$\left\{\begin{array}{l}{3x+y=8}\\{x+2y=m}\end{array}\right.$有相同的解，可知兩個(gè)方程組的解適合方程組中的每個(gè)方程，從而可得方程組$\left\{\begin{array}{l}{x=3}\\{3x+y=8}\end{array}\right.$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，本題得以解決．

解答 解：∵方程組$\left\{\begin{array}{l}{x+y=n}\\{x=3}\end{array}\right.$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，$\left\{\begin{array}{l}{x=3}\\{y=-1}\end{array}\right.$
將$\left\{\begin{array}{l}{x=3}\\{y=-1}\end{array}\right.$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．

點(diǎn)評(píng) 本題考查二元一次方程組的解，解題關(guān)鍵是明確如果兩個(gè)方程組的解相同，則這組解適合兩個(gè)方程組中的任何一個(gè)方程．