Question

9．在解決關于x，y的二元一次方程組$\left\{\begin{array}{l}{ax+by=3}\\{cx-3y=5}\end{array}\right.$時，小明由于粗心，把c寫錯解得$\left\{\begin{array}{l}{x=-1}\\{y=1}\end{array}\right.$，小紅正確地解得$\left\{\begin{array}{l}{x=4}\\{y=-3}\end{array}\right.$，求a²b-ab²-c的值．

Answer 1

分析 先把正確的解代入求出c的值，然后再把解$\left\{\begin{array}{l}{x=-1}\\{y=1}\end{array}\right.$與$\left\{\begin{array}{l}{x=4}\\{y=-3}\end{array}\right.$代入ax+by=3得到關于a，b的方程組，再代入代數(shù)式計算即可得出答案．

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，
由題意得：把$\left\{\begin{array}{l}{x=-1}\\{y=1}\end{array}\right.$與$\left\{\begin{array}{l}{x=4}\\{y=-3}\end{array}\right.$代入①得$\left\{\begin{array}{l}{4a-3b=3}\\{-a+b=3}\end{array}\right.$，
解方程組得：$\left\{\begin{array}{l}{a=12}\\{b=15}\end{array}\right.$，
把a=12，b=15，c=-1代入得
a²b-ab²-c=12×12×15-12×15×15-（-1）=-539．

點評 本題考查了二元一次方程組的解，難度適中，關鍵是對題中已知條件的正確理解與把握．