Question

10．关于x，y的方程2x=8-y的正整数解的组数为$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=4}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=6}\end{array}\right.$．

Answer 1

分析 用y表示出x，即可确定出方程的正整数解．

解答 解：方程整理得：x=$\frac{8-y}{2}$=4-$\frac{y}{2}$，
当y=2时，x=4-1=3；当y=4时，x=4-2=2；当y=6时，x=4-3=1，
则方程的正整数解为$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=4}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=6}\end{array}\right.$，
故答案为：$\left\{\begin{array}{l}{x=3}\\{y=2}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=4}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=6}\end{array}\right.$

点评 此题考查了二元一次方程的解，方程的解即为能使方程左右两边相等的未知数的值．