Question

3．方程3x+2y=13的所有正整数解是$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$．

Answer 1

分析 把y看做已知数表示出x，即可确定出正整数解．

解答 解：方程3x+2y=13，
解得：x=$\frac{13-2y}{3}$，
当y=2时，x=3；y=5时，x=1，
则方程的所有正整数解为$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$．
故答案为：$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$．

点评 此题考查了解二元一次方程，解题的关键是将y看做已知数求出x．