若x、y、z满足3x+7y+z=1和4x+10y+z=2001，则分式2000x+2000y+2000zx+3y的值为．

Question

若x、y、z满足3x+7y+z=1和4x+10y+z=2001，则分式(2000x+2000y+2000z)/(x+3y)的值为______．

Answer 1

由x、y、z满足3x+7y+z=1和4x+10y+z=2001，
得出：

2(x+3y)+(x+y+z)＝1

3(x+3y)+(x+y+z)＝2001

，解得：

x+3y＝2000

x+y+z＝−3999

，
∴(2000x+2000y+2000z)/(x+3y)=(2000(x+y+z))/(x+3y)，
=(2000×(−3999))/(2000)=-3999．
故答案为：-3999．