Question

8．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 根据$\left\{\begin{array}{l}{x=4}\\{y=-2}\end{array}\right.$与$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$都是方程kx-b=y的解，可以得到二元一次方程组，解出二元一次方程组的解，即可得到k和b的值．

解答 解：∵$\left\{\begin{array}{l}{x=4}\\{y=-2}\end{array}\right.$与$\left\{\begin{array}{l}{x=1}\\{y=1}\end{array}\right.$都是方程kx-b=y的解，
∴$\left\{\begin{array}{l}{4k-b=-2}\\{k-b=1}\end{array}\right.$，
解得，$\left\{\begin{array}{l}{k=-1}\\{b=-2}\end{array}\right.$，
即k的值是-1，b的值是-2．

点评 本题考查二元一次方程的解，解题的关键是明确二元一次方程的解一定适合二元一次方程．