Question

11．兩位同學在解方程組時，甲同學由$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$正確地解出$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，乙同學因把C寫錯了解得 $\left\{\begin{array}{l}x=-2\\ y=2\end{array}\right.$，那么a、b、c的正確的值應為多少？

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，組成方程組$\left\{\begin{array}{l}{3a-2b=2}\\{3c+14=8}\\{-2a+2b=2}\end{array}\right.$，解方程組即可．

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：$\left\{\begin{array}{l}{a=4}\\{b=5}\\{c=-2}\end{array}\right.$．

點評 本題考查了二元一次方程組的解，解決本題的關鍵是組成三元一次方程組．