Question

19．方程2x+y=7的正整數(shù)解是$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，$\left\{\begin{array}{l}{x=3}\\{y=1}\end{array}\right.$．

Answer 1

分析 把x看做已知數(shù)表示出y，即可確定出正整數(shù)解．

解答 解：方程2x+y=7，
解得：y=-2x+7，
當(dāng)x=1時(shí)，y=5；當(dāng)x=2時(shí)，y=3；當(dāng)x=3時(shí)，y=1，
則方程的正整數(shù)解為$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，$\left\{\begin{array}{l}{x=3}\\{y=1}\end{array}\right.$．
故答案為：$\left\{\begin{array}{l}{x=1}\\{y=5}\end{array}\right.$，$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，$\left\{\begin{array}{l}{x=3}\\{y=1}\end{array}\right.$

點(diǎn)評(píng) 此題考查了解二元一次方程，解題的關(guān)鍵是將x看作已知數(shù)求出y．