Question

6．已知$\left\{\begin{array}{l}{x=4}\\{y=-2}\end{array}\right.$与$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$都是方程kx+b=y的解，求k和b的值．

Answer 1

分析 把$\left\{\begin{array}{l}{x=4}\\{y=-2}\end{array}\right.$与$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$代入方程kx+b=y，得到关于k、b的方程，解之可得．

解答 解：把$\left\{\begin{array}{l}{x=4}\\{y=-2}\end{array}\right.$与$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$代入方程kx+b=y，得：$\left\{\begin{array}{l}{4k+b=-2}\\{k+b=1}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{k=-1}\\{b=2}\end{array}\right.$，
答：k的值为-1，b的值为2．

点评 本题主要考查二元一次方程组的解和解二元一次方程组的能力，熟练掌握二元一次方程组的解得定义得到关于k、b的方程组是解题的关键．