Question

3．已知关于x，y的二元一次方程组$\left\{\begin{array}{l}{ax-by=4}\\{ax+by=6}\end{array}\right.$与方程组$\left\{\begin{array}{l}{3x-y=5}\\{4x-7y=1}\end{array}\right.$的解相同，则2a-b=4．

Answer 1

分析 根据二元一次方程组的解法即可求出答案．

解答 解：$\left\{\begin{array}{l}{3x-y=5}\\{4x-7y=1}\end{array}\right.$
解得：$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$
将$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入$\left\{\begin{array}{l}{ax-by=4}\\{ax+by=6}\end{array}\right.$
得：$\left\{\begin{array}{l}{2a-b=4}\\{2a+b=6}\end{array}\right.$
∴2a-b=4
故答案为：4

点评 本题考查二元一次方程组的解法，解题的关键是熟练运用二元一次方程组的解法，本题属于基础题型．