Question

8．方程x+3y=7的非负整数解是$\left\{\begin{array}{l}{x=7}\\{y=0}\end{array}\right.$，$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=2}\end{array}\right.$．

Answer 1

分析 把y看做已知数表示出x，即可确定出非负整数解．

解答 解：方程x+3y=7，
解得：x=-3y+7，
当y=0时，x=7；当y=1时，x=4；当y=2时，x=1，
则方程的非负整数解为$\left\{\begin{array}{l}{x=7}\\{y=0}\end{array}\right.$，$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=2}\end{array}\right.$．
故答案为：$\left\{\begin{array}{l}{x=7}\\{y=0}\end{array}\right.$，$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$，$\left\{\begin{array}{l}{x=1}\\{y=2}\end{array}\right.$

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．