Question

15．若方程组$\left\{\begin{array}{l}{ax-2y=1}\\{2x+by=5}\end{array}\right.$的解是$\left\{\begin{array}{l}{x=1}\\{y=a}\end{array}\right.$，则b=-3．

Answer 1

分析 把$\left\{\begin{array}{l}{x=1}\\{y=a}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax-2y=1}\\{2x+by=5}\end{array}\right.$得：$\left\{\begin{array}{l}{a-2a=1}\\{2+ab=5}\end{array}\right.$，解方程组即可．

解答 解：把$\left\{\begin{array}{l}{x=1}\\{y=a}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax-2y=1}\\{2x+by=5}\end{array}\right.$得：
$\left\{\begin{array}{l}{a-2a=1}\\{2+ab=5}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=-1}\\{b=-3}\end{array}\right.$，
故答案为：-3．

点评 本题考查了二元一次方程组的解，解集本题的关键是运用代入法求解．