Question

4．两个学生解方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$甲正确得出：$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，乙把c写错，解得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，求a、b、c．

Answer 1

分析 根据方程组的解的定义得到关于a、b、c的方程组，再进一步运用加减消元法求解．

解答 解：把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$得；$\left\{\begin{array}{l}{3a-2b=2}\\{3c+14=8}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入ax+by=2得：-2a+2b=2，
可组成方程组$\left\{\begin{array}{l}{3a-2b=2}\\{3c+14=8}\\{-2a+2b=2}\end{array}\right.$，
解得；$\left\{\begin{array}{l}{a=4}\\{b=5}\\{c=-2}\end{array}\right.$．

点评 本题考查了二元一次方程组的解，以及三元一次方程组的解法，正确解方程组是关键．