Question

8．解方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$时，某同学把c看错后得到$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，而正确的解是$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，那么a、b、c的值是（　　）

• A． a=4，b=5，c=2
• B． a，b，c的值不能确定
• C． a=4，b=5，c=-2
• D． a，b不能确定，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$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$得出$\left\{\begin{array}{l}{3a-2b=2②}\\{3c+14=8③}\end{array}\right.$解方程组③求出c，解由①②组成的方程组，求出a、b，即可得出选项．

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

点评 本题考查了二元一次方程组的解，解二元一次方程组的应用，能理解二元一次方程组解的定义是解此题的关键．