Question

13．已知$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，$\left\{\begin{array}{l}{x=3}\\{y=3}\end{array}\right.$，都是方程y=kx+b的解，则k和b的值是（　　）

• A． $\left\{\begin{array}{l}{k=1}\\{b=2}\end{array}\right.$
• B． $\left\{\begin{array}{l}{k=0}\\{b=-1}\end{array}\right.$
• C． $\left\{\begin{array}{l}{k=2}\\{b=-3}\end{array}\right.$
• D． $\left\{\begin{array}{l}{k=1}\\{b=-2}\end{array}\right.$

Answer 1

分析 把$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$和$\left\{\begin{array}{l}{x=3}\\{y=3}\end{array}\right.$代入方程，得出一个关于k、b的方程组，求出方程组的解即可．

解答 解：∵$\left\{\begin{array}{l}{x=2}\\{y=1}\end{array}\right.$，$\left\{\begin{array}{l}{x=3}\\{y=3}\end{array}\right.$，都是方程y=kx+b的解，
∴代入得：$\left\{\begin{array}{l}{2k+b=1}\\{3k+b=3}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{k=2}\\{b=-3}\end{array}\right.$，
故选C．

点评 本题考查了二元方程组的解和解二元一次方程组，能得出关于k、b的方程组是解此题的关键．