Question

10．两位同学在解方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$时，甲正确地解出方程组为$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，乙因为把c写错了而解得的解为$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$，已知乙没有再发生其他错误，请确定a，b，c的值．

Answer 1

分析 根据题意可知$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$是ax+by=2的解，从而可求出a与b的值，由因为$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$是cx-7y=8的解，所以可求出c的值．

解答 解：由题意可知：$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$是cx-7y=8的解，
∴3c+14=8，
∴c=-2
由题意可知：$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$是ax+by=2的解，
∴$\left\{\begin{array}{l}{3a-2b=2}\\{-2a+2b=2}\end{array}\right.$
解得：$\left\{\begin{array}{l}{a=4}\\{b=5}\end{array}\right.$

点评 本题考查二元一次方程的解，解题的关键是熟练二元一次方程组的解法，本题属于基础题型．