Question

4．已知關(guān)于x，y的方程組$\left\{{\begin{array}{l}{ax+by=10}\\{mx-ny=8}\end{array}}\right.$的解是$\left\{{\begin{array}{l}{x=1}\\{y=2}\end{array}}\right.$，則關(guān)于x，y的方程組$\left\{{\begin{array}{l}{\frac{1}{2}a（x+y）+\frac{1}{3}b（x-y）=10}\\{\frac{1}{2}m（x+y）-\frac{1}{3}n（x-y）=8}\end{array}}\right.$的解為（　�。�

• A． $\left\{{\begin{array}{l}{x=1}\\{y=2}\end{array}}\right.$
• B． $\left\{{\begin{array}{l}{x=2}\\{y=1}\end{array}}\right.$
• C． $\left\{{\begin{array}{l}{x=4}\\{y=-2}\end{array}}\right.$
• D． $\left\{{\begin{array}{l}{x=3}\\{y=2}\end{array}}\right.$

Answer 1

分析 把所求方程組轉(zhuǎn)化為關(guān)于a、b的形式，然后根據(jù)已知方程組的解列出關(guān)于x、y的方程組的解，再求解即可．

解答 解：方程組變形為$\left\{\begin{array}{l}{a•\frac{x+y}{2}+b•\frac{x-y}{3}=10}\\{m•\frac{x+y}{2}+n•\frac{x-y}{3}=8}\end{array}\right.$，
∵關(guān)于x，y的方程組$\left\{{\begin{array}{l}{ax+by=10}\\{mx-ny=8}\end{array}}\right.$的解是$\left\{{\begin{array}{l}{x=1}\\{y=2}\end{array}}\right.$，
∴所求的方程組中$\left\{\begin{array}{l}{\frac{x+y}{2}=1}\\{\frac{x-y}{3}=2}\end{array}\right.$，
整理得，$\left\{\begin{array}{l}{x+y=2}\\{x-y=6}\end{array}\right.$，
解得$\left\{\begin{array}{l}{x=4}\\{y=-2}\end{array}\right.$，
即所求方程組的解是$\left\{\begin{array}{l}{x=4}\\{y=-2}\end{array}\right.$．
故選C．

點(diǎn)評(píng) 本題考查了二元一次方程組的解，把所求方程整理成關(guān)于a、b、m、n的形式，并列出關(guān)于x、y的方程組是解題的關(guān)鍵，整體思想的利用是解題的關(guān)鍵．