Question

18．已知$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=4}\end{array}\right.$都是方程y=kx+b的解，则k和b的值是（　　）

• A． $\left\{\begin{array}{l}{k=-\frac{1}{2}}\\{b=3}\end{array}\right.$
• B． $\left\{\begin{array}{l}{k=-\frac{1}{2}}\\{b=-1}\end{array}\right.$
• C． $\left\{\begin{array}{l}{k=\frac{1}{2}}\\{b=-1}\end{array}\right.$
• D． $\left\{\begin{array}{l}{k=\frac{1}{2}}\\{b=5}\end{array}\right.$

Answer 1

分析 根据方程的解的定义，可把$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=4}\end{array}\right.$代入方程y=kx+b，得到关于k，b的方程组，解方程组即可．

解答 解：把$\left\{\begin{array}{l}{x=4}\\{y=1}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=4}\end{array}\right.$代入方程y=kx+b，
得$\left\{\begin{array}{l}{4k+b=1}\\{-2k+b=4}\end{array}\right.$，
解之得$\left\{\begin{array}{l}{k=-\frac{1}{2}}\\{b=3}\end{array}\right.$．
故选A．

点评 本题考查了二元一次方程的解，理解方程的解的定义，会解方程组是关键．