Question

15．解方程組$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$時(shí)，一學(xué)生把c看錯(cuò)而得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，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． 不能確定
• B． 4，5，-2
• C． 4，7，2
• D． 4，7，-2

Answer 1

分析 把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入方程組$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$得出3a-2b=2，3c-7×（-2）=8，-2a+2b=2，求得c，建立a、b的方程組求得a、b即可．

解答 解：$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入方程組$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$得
3a-2b=2，3c-7×（-2）=8，-2a+2b=2，
因此c=-2，$\left\{\begin{array}{l}{3a-2b=2}\\{-2a+2b=2}\end{array}\right.$，
解得：a=4，b=5，c=-2．
故選：B．

點(diǎn)評 此題主要考查了二元一次方程組的解，掌握解二元一次方程組的方法是解決問題的關(guān)鍵．