解方程组$\left\{\begin{array}{l}{ax+by=6}\\{cx-4y=-2}\end{array}\right.$.小明正确解得$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$.小丽只看错了c解得$\left\{\begin{array}{l}{x=-2}\\{y=1}\end{array}\right.$.则� 题目和参考答案——青夏教育精英家教网—

题目内容

8．解方程组$\left\{\begin{array}{l}{ax+by=6}\\{cx-4y=-2}\end{array}\right.$，小明正确解得$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，小丽只看错了c解得$\left\{\begin{array}{l}{x=-2}\\{y=1}\end{array}\right.$，则当x=-1时，代数式ax²-bx+c的值为6.5．

分析把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=6}\\{cx-4y=-2}\end{array}\right.$得出$\left\{\begin{array}{l}{2a+3b=6①}\\{2c-12=-2②}\end{array}\right.$，求出c，把$\left\{\begin{array}{l}{x=-2}\\{y=1}\end{array}\right.$代入ax+by=6得出-2a+b=6③，由①和③组成方程组，求出a、b值，最后代入求出即可．

解答解：把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入方程组$\left\{\begin{array}{l}{ax+by=6}\\{cx-4y=-2}\end{array}\right.$得：$\left\{\begin{array}{l}{2a+3b=6①}\\{2c-12=-2②}\end{array}\right.$，
解②得：c=5，
把$\left\{\begin{array}{l}{x=-2}\\{y=1}\end{array}\right.$代入ax+by=6得：-2a+b=6③，
由①和③组成方程组$\left\{\begin{array}{l}{2a+3b=6}\\{-2a+b=6}\end{array}\right.$，
解得：a=-1.5，b=3，
当x=-1时，ax²-bx+c=-1.5×（-1）²-3×（-1）+5=6.5，
故答案为：6.5．

点评本题考查了解二元一次方程组，二元一次方程组的解等知识点，能求出a、b、c的值是解此题的关键．