因为x^2+xy+y=59,y^2+xy+x=51
所以两式相加,x^2+xy+y+(y^2+xy+x)=59+51=110
所以,(x^2+2xy+y^2)+(x+y)-110=0
所以,(x+y)^2+(x+y)-110=0
所以,(x+y+11)(x+y-10)=0
所以,x+y=-11或x+y=10
两式相减,x^2+xy+y-(y^2+xy+x)=59-51=8
所以,(x^2-y^2)-(x-y)-8=0
所以,(x-y)(x+y)-(x-y)-8=0
所以,(x-y)(x+y-1)-8=0
当x+y=-11时,(x-y)(x+y-1)-8=(x-y)(-11-1)-8=0
则x-y=-2/3,联立x+y=-11,解得x=-35/6,y=-31/6
当x+y=10时,(x-y)(x+y-1)-8=(x-y)(10-1)-8=0
则x-y=8/9,联立x+y=10,解得x=49/9,y=41/9