Question

11．已知方程組$\left\{\begin{array}{l}{ax+by=3}\\{5x-cy=1}\end{array}\right.$，甲得正確的解$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，丙乙比較粗心，把c給看錯了，解得$\left\{\begin{array}{l}x=3\\ y=6\end{array}$，則a+b+c=5．

Answer 1

分析 由題意可得$\left\{\begin{array}{l}{2a+3b=3①}\\{10-3c=1②}\end{array}\right.$，3a+6b=3③，然后解方程組即可求得答案．

解答 解：∵方程組$\left\{\begin{array}{l}{ax+by=3}\\{5x-cy=1}\end{array}\right.$，甲得正確的解$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，
∴$\left\{\begin{array}{l}{2a+3b=3①}\\{10-3c=1②}\end{array}\right.$，
∵丙乙比較粗心，把c給看錯了，解得$\left\{\begin{array}{l}x=3\\ y=6\end{array}$，
∴3a+6b=3③，
聯(lián)立①③得：a=3，b=-1，c=3．
∴a+b+c=5．
故答案為：5．

點評 此題考查了二元一次方程組的解法．注意根據(jù)題意得到新方程組是關鍵．