Question

11．两位同学在解方程组时，甲同学由$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$正确地解出$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，乙同学因把C写错了解得 $\left\{\begin{array}{l}x=-2\\ y=2\end{array}\right.$，那么a、b、c的正确的值应为多少？

Answer 1

分析 把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$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，组成方程组$\left\{\begin{array}{l}{3a-2b=2}\\{3c+14=8}\\{-2a+2b=2}\end{array}\right.$，解方程组即可．

解答 解：把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$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，
∴$\left\{\begin{array}{l}{3a-2b=2}\\{3c+14=8}\\{-2a+2b=2}\end{array}\right.$，
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，解决本题的关键是组成三元一次方程组．