已知{x+2y=2009, y+2z=2010, z+2x=2011,则x+y+z=_______.
问题描述:
已知{x+2y=2009, y+2z=2010, z+2x=2011,则x+y+z=_______.
答
∵x+2y=2009,y+2z=2010,z+2x=2011
∴x+2y+ y+2z+z+2x=2009+2010+2011
∴3x+3y+3z=6030
即3(x+y+z)=6030
∴x+y+z=2010