Question

3．方程3x+2y=13的所有正整數(shù)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看做已知數(shù)表示出x，即可確定出正整數(shù)解．

解答 解：方程3x+2y=13，
解得：x=$\frac{13-2y}{3}$，
當y=2時，x=3；y=5時，x=1，
則方程的所有正整數(shù)解為$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$．
故答案為：$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$．

點評 此題考查了解二元一次方程，解題的關(guān)鍵是將y看做已知數(shù)求出x．