Question

19．已知甲、乙二人解關(guān)于x、y的方程組$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$，甲正確地解出$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，而乙把c抄錯了，結(jié)果解得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，求a、b、c的值．

Answer 1

分析 根據(jù)甲正確地解得$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，?代入原方程組，根據(jù)乙僅因抄錯了題中的c，解得$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，代入第一個方程，三個方程組成方程組即可得到結(jié)果．

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

點評 本題考查了方程組的解的定義，正確列出關(guān)于a、b、c的方程組，解方程組是關(guān)鍵．