Question

8．解方程組$\left\{\begin{array}{l}{ax+by=6}\\{cx-4y=-2}\end{array}\right.$，小明正確解得$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，小麗只看錯了c解得$\left\{\begin{array}{l}{x=-2}\\{y=1}\end{array}\right.$，則當x=-1時，代數(shù)式ax²-bx+c的值為6.5．

Answer 1

分析 把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入方程組$\left\{\begin{array}{l}{ax+by=6}\\{cx-4y=-2}\end{array}\right.$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組成方程組，求出a、b值，最后代入求出即可．

解答 解：把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入方程組$\left\{\begin{array}{l}{ax+by=6}\\{cx-4y=-2}\end{array}\right.$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組成方程組$\left\{\begin{array}{l}{2a+3b=6}\\{-2a+b=6}\end{array}\right.$，
解得：a=-1.5，b=3，
當x=-1時，ax²-bx+c=-1.5×（-1）²-3×（-1）+5=6.5，
故答案為：6.5．

點評 本題考查了解二元一次方程組，二元一次方程組的解等知識點，能求出a、b、c的值是解此題的關鍵．