Question

14．小明與小穎解同一道關(guān)于x，y的方程組$\left\{\begin{array}{l}{mx+5y=15①}\\{2x+ny=-1②}\end{array}\right.$，小明把方程①抄錯，求得的解為$\left\{\begin{array}{l}{x=-3}\\{y=-1}\end{array}\right.$，小穎把方程②抄錯，求得的解為$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$，求原方程組的解．

Answer 1

分析 根據(jù)題意把$\left\{\begin{array}{l}x=-3\\ y=-1\end{array}\right.$代入方程②，把$\left\{\begin{array}{l}x=5\\ y=4\end{array}\right.$代入方程①得出關(guān)于n、m的方程組，求出m、n的值，再解出原方程組的解即可．

解答 解：∵小明把方程①抄錯，求得的解為$\left\{\begin{array}{l}{x=-3}\\{y=-1}\end{array}\right.$，小穎把方程②抄錯，求得的解為$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$，
∴$\left\{\begin{array}{l}-6-n=-1①\\ 5m+20=15②\end{array}\right.$，解得$\left\{\begin{array}{l}m=-1\\ n=-5\end{array}\right.$，
∴原方程組為$\left\{\begin{array}{l}-x+5y=15\\ 2x-5y=-1\end{array}\right.$，解得$\left\{\begin{array}{l}x=14\\ y=\frac{29}{5}\end{array}\right.$．

點評 本題考查的是二元一次方程組的解，先根據(jù)題意得出m，n的值是解答此題的關(guān)鍵．