Question

5．已知$\left\{\begin{array}{l}{x=a}\\{y=b}\end{array}\right.$是方程组$\left\{\begin{array}{l}{|x|=2}\\{2x+y=3}\end{array}\right.$的解，则a+b等于（　　）

• A． 1
• B． 5
• C． 1或5
• D． 0

Answer 1

分析 把$\left\{\begin{array}{l}{x=a}\\{y=b}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{|x|=2}\\{2x+y=3}\end{array}\right.$，求出a，b的值，再代入求解即可．

解答 解：∵$\left\{\begin{array}{l}{x=a}\\{y=b}\end{array}\right.$是方程组$\left\{\begin{array}{l}{|x|=2}\\{2x+y=3}\end{array}\right.$的解，
∴$\left\{\begin{array}{l}{|a|=2}\\{2a+b=3}\end{array}\right.$，解得$\left\{\begin{array}{l}{a=2}\\{b=-1}\end{array}\right.$或$\left\{\begin{array}{l}{a=-2}\\{b=7}\end{array}\right.$，
∴a+b=1或5，
故选：C．

点评 本题主要考查了二元一次方程组的解，解题的关键是求出a，b的值．