Question

17．若二元一次方程组$\left\{\begin{array}{l}{ax-2016y=2015}\\{2016x-by=2017}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，则二元一次方程组$\left\{\begin{array}{l}{a（x-y）-2016（x+y）=2015}\\{2016（x-y）-b（x+y）=2017}\end{array}\right.$的解是（　　）

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

Answer 1

分析 根据题意将x，y的值代入方程组$\left\{\begin{array}{l}{ax-2016y=2015}\\{2016x-by=2017}\end{array}\right.$，得出关于a，b的二元一次方程组，求得a、b的值，然后代入方程组$\left\{\begin{array}{l}{a（x-y）-2016（x+y）=2015}\\{2016（x-y）-b（x+y）=2017}\end{array}\right.$，解方程组求出即可．

解答 解：∵二元一次方程组$\left\{\begin{array}{l}{ax-2016y=2015}\\{2016x-by=2017}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，
∴$\left\{\begin{array}{l}{2a-2016=2015}\\{4032-b=2017}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=2015.5}\\{b=2015}\end{array}\right.$，
代入方程组$\left\{\begin{array}{l}{a（x-y）-2016（x+y）=2015}\\{2016（x-y）-b（x+y）=2017}\end{array}\right.$得$\left\{\begin{array}{l}{2015.5（x-y）-2016（x+y）=2015}\\{2016（x-y）-2015（x+y）=2017}\end{array}\right.$，
解得$\left\{\begin{array}{l}{x=\frac{3}{2}}\\{y=-\frac{1}{2}}\end{array}\right.$
故选C．

点评 此题主要考查了二元一次方程组的解法，熟练掌握二元一次方程组的解法是解题关键．