Question

6．解方程组$\left\{\begin{array}{l}{ax+by=6}\\{cx-4y=-2}\end{array}\right.$时，小强正确解得$\left\{\begin{array}{l}{x=2}\\{y=2}\end{array}\right.$，而小刚只看错了C，解得$\left\{\begin{array}{l}{x=-2}\\{y=4}\end{array}\right.$，则当x=-1时，ax²+bx+c的值是（　　）

• A． 6
• B． 2
• C． 0
• D． -8

Answer 1

分析 根据题意把$\left\{\begin{array}{l}{x=2}\\{y=2}\end{array}\right.$和$\left\{\begin{array}{l}{x=-2}\\{y=4}\end{array}\right.$代入ax+by=6组成方程组，解方程组求出a、b的值，把$\left\{\begin{array}{l}{x=2}\\{y=2}\end{array}\right.$代入cx-4y=-2求出c，计算得到答案．

解答 解：由题意得，
$\left\{\begin{array}{l}{2a+2b=6}\\{-2a+4b=6}\end{array}\right.$，
解得，$\left\{\begin{array}{l}{a=1}\\{b=2}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=2}\\{y=2}\end{array}\right.$代入cx-4y=-2，得c=3，
当x=-1时，x²+2x+3=2，
故选：B．

点评 本题考察的是二元一次方程组的解的定义和解法，正确理解题意组成新的方程组是解题的关键．