Question

8．解方程組$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$時(shí)，某同學(xué)把c看錯(cuò)后得到$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，而正確的解是$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，那么a、b、c的值是（　�。�

• A． a=4，b=5，c=2
• B． a，b，c的值不能確定
• C． a=4，b=5，c=-2
• D． a，b不能確定，c=-2

Answer 1

分析 把$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入方程ax+by=2求出a-b=-1①，把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入方程組$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$得出$\left\{\begin{array}{l}{3a-2b=2②}\\{3c+14=8③}\end{array}\right.$解方程組③求出c，解由①②組成的方程組，求出a、b，即可得出選項(xiàng)．

解答 解：把$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入方程ax+by=2得：-2a+2b=2，
a-b=-1①，
把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入方程組$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$得：$\left\{\begin{array}{l}{3a-2b=2②}\\{3c+14=8③}\end{array}\right.$
解方程組③得：c=-2，
解由①②組成的方程組$\left\{\begin{array}{l}{a-b=-1}\\{3a-2b=2}\end{array}\right.$得：a=4，b=5，
故選C．

點(diǎn)評(píng) 本題考查了二元一次方程組的解，解二元一次方程組的應(yīng)用，能理解二元一次方程組解的定義是解此題的關(guān)鍵．