Question

14．甲、乙两人同解方程组$\left\{\begin{array}{l}{Ax+By=2}\\{Cx+3y=-2}\end{array}\right.$，甲正确解得$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$，乙因抄错C解得$\left\{\begin{array}{l}{x=2}\\{y=-6}\end{array}\right.$，求A+B-C的值．

Answer 1

分析 根据方程组的解的定义得到关于A、B、C的方程组，再进一步运用加减消元法求解．

解答 解：把$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$代入原方程组，得
$\left\{\begin{array}{l}{A-B=2}\\{C-3=-2}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=2}\\{y=-6}\end{array}\right.$代入Ax+By=2，得
2A-6B=2．
可组成方程组$\left\{\begin{array}{l}{A-B=2}\\{C-3=-2}\\{2A-6B=2}\end{array}\right.$，
解得$\left\{\begin{array}{l}{A=2.5}\\{B=0.5}\\{C=1}\end{array}\right.$，
则A+B-C=2．

点评 此题考查二元一次方程组的解，关键是明白二元一次方程组的解的定义以及方程组的解法．