Question

10．小明和小文解一個二元一次組$\left\{\begin{array}{l}cx-3y=-2\\ ax+by=2\end{array}\right.$小明正確解得$\left\{\begin{array}{l}x=1\\ y=-1\end{array}\right.$小文因抄錯了c，解得$\left\{\begin{array}{l}x=2\\ y=-6.\end{array}\right.$已知小文除抄錯了c外沒有發(fā)生其他錯誤，求a+b+c的值．

Answer 1

分析 把$\left\{\begin{array}{l}{x=1}\\{y=-1}\end{array}\right.$代入方程組第一個方程求出c的值，將x與y的兩對值代入第二個方程求出a與b的值，即可求出a+b+c的值．

解答 解：把$\left\{\begin{array}{l}x=1\\ y=-1\end{array}\right.$代入cx-3y=-2，得c+3=-2，
解得：c=-5，
把$\left\{\begin{array}{l}x=1\\ y=-1\end{array}\right.$與$\left\{\begin{array}{l}x=2\\ y=-6\end{array}\right.$分別代入ax+by=2，得$\left\{\begin{array}{l}a-b=2\\ 2a-6b=2.\end{array}\right.$，
解得：$\left\{\begin{array}{l}a=2\frac{1}{2}\\ b=\frac{1}{2}.\end{array}\right.$，
則a+b+c=2$\frac{1}{2}$+$\frac{1}{2}$-5=3-5=-2．

點(diǎn)評 此題考查了二元一次方程組的解，方程組的解即為能使方程組中兩方程成立的未知數(shù)的值．