Question

9．在解决关于x，y的二元一次方程组$\left\{\begin{array}{l}{ax+by=3}\\{cx-3y=5}\end{array}\right.$时，小明由于粗心，把c写错解得$\left\{\begin{array}{l}{x=-1}\\{y=1}\end{array}\right.$，小红正确地解得$\left\{\begin{array}{l}{x=4}\\{y=-3}\end{array}\right.$，求a²b-ab²-c的值．

Answer 1

分析 先把正确的解代入求出c的值，然后再把解$\left\{\begin{array}{l}{x=-1}\\{y=1}\end{array}\right.$与$\left\{\begin{array}{l}{x=4}\\{y=-3}\end{array}\right.$代入ax+by=3得到关于a，b的方程组，再代入代数式计算即可得出答案．

解答 解：$\left\{\begin{array}{l}{ax+by=3①}\\{cx-3y=5②}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=4}\\{y=-3}\end{array}\right.$代入②得：4c-3×（-3）=5，
解得：c=-1，
由题意得：把$\left\{\begin{array}{l}{x=-1}\\{y=1}\end{array}\right.$与$\left\{\begin{array}{l}{x=4}\\{y=-3}\end{array}\right.$代入①得$\left\{\begin{array}{l}{4a-3b=3}\\{-a+b=3}\end{array}\right.$，
解方程组得：$\left\{\begin{array}{l}{a=12}\\{b=15}\end{array}\right.$，
把a=12，b=15，c=-1代入得
a²b-ab²-c=12×12×15-12×15×15-（-1）=-539．

点评 本题考查了二元一次方程组的解，难度适中，关键是对题中已知条件的正确理解与把握．