Question

9．已知方程组$\left\{\begin{array}{l}{ax+by=4}\\{bx+ay=5}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，则a-b的值为-1．

Answer 1

分析 把$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=4}\\{bx+ay=5}\end{array}\right.$中，得出关于a，b的方程组，解答即可．

解答 解：把$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=4}\\{bx+ay=5}\end{array}\right.$中，
可得：$\left\{\begin{array}{l}{2a+b=4}\\{2b+a=5}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=1}\\{b=2}\end{array}\right.$，
把a=1，b=2代入a-b=-1；
故答案为：-1．

点评 此题考查方程组的解，关键是把解代入得出新的方程组．