Question

18．已知方程組 $\left\{\begin{array}{l}{ax+by=3}\\{5x-cy=1}\end{array}\right.$，甲正確地解得$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，而乙粗心地把C看錯了，得$\left\{\begin{array}{l}{x=3}\\{y=6}\end{array}\right.$，試求出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即可得到一個關(guān)于a，b的方程組，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：根據(jù)題意得：$\left\{\begin{array}{l}{2a+3b=3}\\{3a+6b=3}\end{array}\right.$，
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．

點(diǎn)評 本題考查了二元一次方程組的解，方程的解的定義，正確理解定義是解題的關(guān)鍵．