Question

12．解方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$时，一学生把c看错而得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，而正确的解是$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，那么a=4，b=5，c=-2．

Answer 1

分析 首先把$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$和$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入ax+by=2，再把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入cx-7y=8可得$\left\{\begin{array}{l}{-2a+2b=2①}\\{3a-2b=2②}\\{3c+14=8③}\end{array}\right.$，再解即可．

解答 解：由题意得：$\left\{\begin{array}{l}{-2a+2b=2①}\\{3a-2b=2②}\\{3c+14=8③}\end{array}\right.$，
解③得：c=-2；
①+②得：a=4，
把a=4代入①得：-8+2b=2，
解得：b=5，
故答案为：4；5；-2．

点评 此题主要考查了二元一次方程组的解，关键是掌握二元一次方程组的两个方程的公共解，叫做二元一次方程组的解．