Question

11．已知方程组$\left\{\begin{array}{l}{ax+by=3}\\{5x-cy=1}\end{array}\right.$，甲得正确的解$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，丙乙比较粗心，把c给看错了，解得$\left\{\begin{array}{l}x=3\\ y=6\end{array}$，则a+b+c=5．

Answer 1

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

解答 解：∵方程组$\left\{\begin{array}{l}{ax+by=3}\\{5x-cy=1}\end{array}\right.$，甲得正确的解$\left\{\begin{array}{l}{x=2}\\{y=3}\end{array}\right.$，
∴$\left\{\begin{array}{l}{2a+3b=3①}\\{10-3c=1②}\end{array}\right.$，
∵丙乙比较粗心，把c给看错了，解得$\left\{\begin{array}{l}x=3\\ y=6\end{array}$，
∴3a+6b=3③，
联立①③得：a=3，b=-1，c=3．
∴a+b+c=5．
故答案为：5．

点评 此题考查了二元一次方程组的解法．注意根据题意得到新方程组是关键．