Question

17．$\left\{\begin{array}{l}{x=5}\\{y=5}\end{array}\right.$和$\left\{\begin{array}{l}{x=2}\\{y=7}\end{array}\right.$都是方程ax-y=b的解，求a与b的值．

Answer 1

分析 把两组解分别代入方程，得关于a，b的方程组，求解即可．

解答 解：将$\left\{\begin{array}{l}{x=5}\\{y=5}\end{array}\right.$和$\left\{\begin{array}{l}{x=2}\\{y=7}\end{array}\right.$都代入方程ax-y=b，得：$\left\{\begin{array}{l}{5a-5=b}\\{2a-7=b}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=-\frac{2}{3}}\\{b=-\frac{25}{3}}\end{array}\right.$．

点评 此题考查了二元一次方程组的解及解二元一次方程组，掌握方程组的解即为能使方程组中两方程成立的未知数的值是解题的关键．