Question

4．解方程组$\left\{\begin{array}{l}{ax+by=2}\\{cx-7y=8}\end{array}\right.$时，应该正确地解得$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$，小明由于看错了系数c，得到的解为$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$则a-b-c=1．

Answer 1

分析 把正确和错误结果代入方程组第一个方程求出a与b的值，将正确结果代入第二个方程求出c的值，即可求出所求．

解答 解：把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$与$\left\{\begin{array}{l}{x=-2}\\{y=2}\end{array}\right.$代入得：$\left\{\begin{array}{l}{3a-2b=2}\\{-a+b=1}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=4}\\{b=5}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=3}\\{y=-2}\end{array}\right.$代入得：3c+14=8，
解得：c=-2，
则a-b-c=4-5+2=1．
故答案为：1

点评 此题考查了二元一次方程组的解，方程组的解即为能使方程组中两方程都成立的未知数的值．