Question

12．已知$\left\{\begin{array}{l}x=-1\\ y=2\end{array}\right.$和$\left\{\begin{array}{l}x=4\\ y=-5\end{array}\right.$是方程ax+by=3的兩個解，則a-b=2．

Answer 1

分析 根據題意得出關于a、b的方程組，求出a、b的值即可得出結論．

解答 解：∵$\left\{\begin{array}{l}x=-1\\ y=2\end{array}\right.$和$\left\{\begin{array}{l}x=4\\ y=-5\end{array}\right.$是方程ax+by=3的兩個解，
∴$\left\{\begin{array}{l}{-a+2b=3}\\{4a-5b=3}\end{array}\right.$，解得$\left\{\begin{array}{l}{a=7}\\{b=5}\end{array}\right.$，
∴a-b=7-5=2．
故答案為：2．

點評 本題考查的是二元一次方程組的解，熟知解二元一次方程組的加減消元法和代入消元法是解答此題的關鍵．