Question

3．甲、乙二人解关于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$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，而乙因把C抄错了，结果解得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，求出a、b、c的值，并求乙将c抄成了何值？

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$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，求代入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$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$，
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：$\left\{\begin{array}{l}{a=4}\\{b=5}\end{array}\right.$，
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4，b的值是5，c的值是-2．

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．