Question

18．已知方程组 $\left\{\begin{array}{l}{ax+by=3}\\{5x-cy=1}\end{array}\right.$，甲正确地解得$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，而乙粗心地把C看错了，得$\left\{\begin{array}{l}{x=3}\\{y=6}\end{array}\right.$，试求出a，b，c的值．

Answer 1

分析 把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，$\left\{\begin{array}{l}{x=3}\\{y=6}\end{array}\right.$代入方程ax+by=3即可得到一个关于a，b的方程组，即可求得a，b的值，把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入方程5x-cy=1即可求得c的值．

解答 解：根据题意得：$\left\{\begin{array}{l}{2a+3b=3}\\{3a+6b=3}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{a=3}\\{b=-1}\end{array}\right.$，
把$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$代入方程5x-cy=1，得到：10-3c=1，
解得：c=3．
故a=3，b=-1 c=3．

点评 本题考查了二元一次方程组的解，方程的解的定义，正确理解定义是解题的关键．