Question

19．已知甲、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$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，而乙把c抄错了，结果解得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，求a、b、c的值．

Answer 1

分析 根据甲正确地解得$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，?代入原方程组，根据乙仅因抄错了题中的c，解得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，代入第一个方程，三个方程组成方程组即可得到结果．

解答 解：由题意得$\left\{\begin{array}{l}{3a-2b=2}\\{-2a+2b=2}\\{3c+14=8}\end{array}\right.$，
解得$\left\{\begin{array}{l}{a=4}\\{b=5}\\{c=-2}\end{array}\right.$．

点评 本题考查了方程组的解的定义，正确列出关于a、b、c的方程组，解方程组是关键．