Question

12．甲、乙两人解关于x、y的方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$，甲正确地解出了$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，而乙把c抄错了，结果得到$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，请你指出乙把c抄成何值，并求出a、b的值．

Answer 1

分析 把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$，由方程组中第二个式子可得：c=-2，然后把解$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入ax+by=2中即可得到答案．

解答 解：把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$中，
可得：$\left\{\begin{array}{l}{3a-2b=2}\\{3c+14=8}\end{array}\right.$，
解得：c=-2，
把$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入ax+by=2中，
可得：-2a+2b=2，
可得新的方程组：$\left\{\begin{array}{l}{3a-2b=2}\\{-2a+2b=2}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=0}\\{b=-1}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入cx-7y=8中，可得：c=11．
答：乙把c抄成了11，a的值是0，b的值是1．

点评 本题考查了二元一次方程组的解，难度适中，关键是对题中已知条件的正确理解与把握．