Question

14．關(guān)于x、y的方程組$\left\{\begin{array}{l}3mx-y=n\\ 2x+ny=m\end{array}\right.$的解是$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$，則（m-n）²等于（　�。�

• A． 25
• B． 3
• C． 4
• D． 1

Answer 1

分析 將x、y的值代入，可得關(guān)于m、n的二元一次方程組，解出m、n的值，代入代數(shù)式即可．

解答 解：把$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$代入方程組$\left\{\begin{array}{l}3mx-y=n\\ 2x+ny=m\end{array}\right.$得：$\left\{\begin{array}{l}{3m-1=n}\\{2+n=m}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{m=-\frac{1}{2}}\\{n=-\frac{5}{2}}\end{array}\right.$
∴$（m-n）^{2}=（-\frac{1}{2}+\frac{5}{2}）^{2}=4$．
故選：C．

點評 此題考查了二元一次方程組的解，解決本題的關(guān)鍵是解二元一次方程組．