Question

16．若方程组$\left\{\begin{array}{l}{2x+y=b}\\{x-by=a}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=1}\\{y=6}\end{array}\right.$，那么|a-b|=55．

Answer 1

分析 把方程组的解代入可分别求得a、b的值，可求得答案．

解答 解：
∵方程组$\left\{\begin{array}{l}{2x+y=b}\\{x-by=a}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=1}\\{y=6}\end{array}\right.$，
∴把$\left\{\begin{array}{l}{x=1}\\{y=6}\end{array}\right.$代入方程组可得$\left\{\begin{array}{l}{2+6=b}\\{1-6b=a}\end{array}\right.$，解得$\left\{\begin{array}{l}{a=-47}\\{b=8}\end{array}\right.$，
∴|a-b|=|-47-8|=|-55|=55，
故答案为：55．

点评 本题主要考查方程组解的定义，根据方程组解的定义求得a、b的值是解题的关键．