Question

5．甲、乙两位同学解同一个关于x，y的二元一次方程组$\left\{\begin{array}{l}{mx+ny=16，①}\\{nx+my=1，②}\end{array}\right.$，甲同学把方程①抄错，求得解为$\left\{\begin{array}{l}{x=-1}\\{y=3}\end{array}\right.$，乙同学把方程②抄错，求得解为$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$，根据上述信息，你能求出原方程组的解吗？如果能，请解方程组；如果不能，请说明理由．

Answer 1

分析 根据题意把$\left\{\begin{array}{l}{x=-1}\\{y=3}\end{array}\right.$代入方程②，把$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$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：把$\left\{\begin{array}{l}{x=-1}\\{y=3}\end{array}\right.$代入方程②，把$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$代入方程①得：
$\left\{\begin{array}{l}{-n+3m=1}\\{3m+2n=16}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{m=2}\\{n=5}\end{array}\right.$，
把m=2，n=5代入原方程组可得：$\left\{\begin{array}{l}{2x+5y=16}\\{5x+2y=1}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{x=-\frac{9}{7}}\\{y=\frac{26}{7}}\end{array}\right.$．

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．