Question

14．小明与小颖解同一道关于x，y的方程组$\left\{\begin{array}{l}{mx+5y=15①}\\{2x+ny=-1②}\end{array}\right.$，小明把方程①抄错，求得的解为$\left\{\begin{array}{l}{x=-3}\\{y=-1}\end{array}\right.$，小颖把方程②抄错，求得的解为$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$，求原方程组的解．

Answer 1

分析 根据题意把$\left\{\begin{array}{l}x=-3\\ y=-1\end{array}\right.$代入方程②，把$\left\{\begin{array}{l}x=5\\ y=4\end{array}\right.$代入方程①得出关于n、m的方程组，求出m、n的值，再解出原方程组的解即可．

解答 解：∵小明把方程①抄错，求得的解为$\left\{\begin{array}{l}{x=-3}\\{y=-1}\end{array}\right.$，小颖把方程②抄错，求得的解为$\left\{\begin{array}{l}{x=5}\\{y=4}\end{array}\right.$，
∴$\left\{\begin{array}{l}-6-n=-1①\\ 5m+20=15②\end{array}\right.$，解得$\left\{\begin{array}{l}m=-1\\ n=-5\end{array}\right.$，
∴原方程组为$\left\{\begin{array}{l}-x+5y=15\\ 2x-5y=-1\end{array}\right.$，解得$\left\{\begin{array}{l}x=14\\ y=\frac{29}{5}\end{array}\right.$．

点评 本题考查的是二元一次方程组的解，先根据题意得出m，n的值是解答此题的关键．