Question

17．如果方程组$\left\{\begin{array}{l}{x=2}\\{ax+by=7}\end{array}\right.$的解与方程组$\left\{\begin{array}{l}{y=3}\\{bx+ay=8}\end{array}\right.$的解相同，则a、b的值是（　　）

• A． $\left\{\begin{array}{l}{a=2}\\{b=1}\end{array}\right.$
• B． $\left\{\begin{array}{l}{a=-2}\\{b=1}\end{array}\right.$
• C． $\left\{\begin{array}{l}{a=2}\\{b=-1}\end{array}\right.$
• D． $\left\{\begin{array}{l}{a=-2}\\{b=-1}\end{array}\right.$

Answer 1

分析 把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=7}\\{bx+ay=8}\end{array}\right.$，得到关于a和b的二元一次方程组，观察方程组的未知数的系数，运用加减法从而求出代数式的值．

解答 解：依题意得：$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$是方程组$\left\{\begin{array}{l}{ax+by=7}\\{bx+ay=8}\end{array}\right.$的解，则$\left\{\begin{array}{l}{2a+3b=7}\\{2b+3a=8}\end{array}\right.$，
解得$\left\{\begin{array}{l}{a=2}\\{b=1}\end{array}\right.$．
故选：A．

点评 此题考查了方程组的解的定义，根据题意得到方程组$\left\{\begin{array}{l}{2a+3b=7}\\{2b+3a=8}\end{array}\right.$是解题的关键．