Question

17．如果方程組$\left\{\begin{array}{l}{x=2}\\{ax+by=7}\end{array}\right.$的解與方程組$\left\{\begin{array}{l}{y=3}\\{bx+ay=8}\end{array}\right.$的解相同，則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$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入方程組$\left\{\begin{array}{l}{ax+by=7}\\{bx+ay=8}\end{array}\right.$，得到關(guān)于a和b的二元一次方程組，觀察方程組的未知數(shù)的系數(shù)，運(yùn)用加減法從而求出代數(shù)式的值．

解答 解：依題意得：$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$是方程組$\left\{\begin{array}{l}{ax+by=7}\\{bx+ay=8}\end{array}\right.$的解，則$\left\{\begin{array}{l}{2a+3b=7}\\{2b+3a=8}\end{array}\right.$，
解得$\left\{\begin{array}{l}{a=2}\\{b=1}\end{array}\right.$．
故選：A．

點(diǎn)評(píng) 此題考查了方程組的解的定義，根據(jù)題意得到方程組$\left\{\begin{array}{l}{2a+3b=7}\\{2b+3a=8}\end{array}\right.$是解題的關(guān)鍵．