Question

20．已知二元一次方程组$\left\{\begin{array}{l}{ax-by=1}\\{bx-ay=7}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，求a、b的值．

Answer 1

分析 将$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax-by=1}\\{bx-ay=7}\end{array}\right.$得$\left\{\begin{array}{l}{2a-b=1}\\{2b-a=7}\end{array}\right.$，解之可得．

解答 解：将$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax-by=1}\\{bx-ay=7}\end{array}\right.$得$\left\{\begin{array}{l}{2a-b=1}\\{2b-a=7}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=3}\\{b=5}\end{array}\right.$．

点评 本题主要考查二元一次方程组的解，根据方程组解的概念得出关于a、b的方程组是解题的关键．