Maple рулит :) набиваем систему и сразу получаем

{x = 1/2*(x3^2*y2-y1*x3^2-y2*y1^2+x2^2*y1+x1^2*y3+y1^2*y3-y1*y3^2-y3*x2^2+y3^2*y2+y2^2*y1-y3*y2^2-y2*x1^2)/(x3*y2-y3*x2-x1*y2+x1*y3+y1*x2-y1*x3), y = -1/2*(x3^2*x2-x3*x2^2-x3*y2^2+y3^2*x2-x1^2*x2+x1^2*x3+x1*x2^2+x1*y2^2-x1*x3^2-x1*y3^2-y1^2*x2+y1^2*x3)/(x3*y2-y3*x2-x1*y2+x1*y3+y1*x2-y1*x3), r = 1/2*RootOf(_Z^2-y3^4*x2^2-4*y3*x1*y2^2*y1*x2+2*x1^3*x3^3+2*x3*y2^2*x1^3-x3^2*x2^4-2*x3*y3^2*x2^2*x1+2*x3*y3^2*x2^3+2*x3^3*x2^3+8*y3^2*x1*y2*y1*x2+2*x1^3*x2^3-4*x3^2*x1*y3*y1*x2-x3^4*y2^2+2*x1*y2^2*y3^2*x2+2*y1^2*x2*x1*y3^2-4*y3*x1^3*x2*y2-4*y3*x1*x2^3*y1-2*x3^2*x2*x1*y2^2-2*x3*y2^2*x1^2*x2+4*x1^2*x2*y1^2*x3-2*x1*x2^2*y1^2*x3+2*x1*y2^2*y1^2*x2-2*x1*x3^2*y1^2*x2+2*x3*x2^4*x1+2*x3*y2^4*x1+2*x1^4*x2*x3+2*x1^3*x2*y2^2-2*x1^3*x2*x3^2-2*x1^2*x2^2*y1^2-2*x1^3*x3*x2^2-2*x1^2*x3^2*y1^2-2*x1^2*x2^2*y2^2+2*x1*x2^3*y1^2+4*x3*x2^2*x1*y2^2+8*x3^2*x1*y2*y1*x2+2*x1*x3^3*y1^2+2*y1^4*x2*x3+2*y2^3*y1^3-x2^4*y1^2-x1^4*y3^2-y1^4*y3^2+2*y1^3*y3^3-y1^2*y3^4-y3^2*x2^4-y3^4*y2^2+2*y3^3*y2^3-y2^4*y1^2-y3^2*y2^4-y2^2*x1^4-y3^4*x1^2-x1^2*y2^4-x1^2*x3^4-y1^4*x2^2-y1^4*x3^2+2*x2^2*y1^3*y3-2*x2^2*y1^2*y3^2+2*x2^4*y1*y3-2*x2^2*y1^2*y2^2-2*x1^2*y3^2*y1^2+2*x1^2*y3^3*y1-2*x1^2*y3^2*x2^2+2*x1^2*y3^3*y2-2*x1^2*y3^2*y2^2+2*x1^4*y3*y2-2*y1^2*y3^3*y2-2*y1^3*y3*y2^2+2*y1*y3^3*x2^2+2*y1*y3^4*y2-2*y1*y3^3*y2^2+2*y3^3*x2^2*y2-2*y3^2*x2^2*y2^2-2*y3^2*y2^3*y1+2*y2^4*y1*y3+2*y2^3*y1*x1^2+2*y3*y2^3*x1^2+2*y3^4*x2*x1-x1^2*x2^4+2*x1^3*x2*y3^2+2*x1*x2^3*y3^2+2*x3^3*x2*y2^2+6*x3^2*x2^2*x1^2-2*x3^2*x2^3*x1+2*x3^4*x2*x1-2*x3^2*x2^2*y2^2-2*x3*x2^3*x1^2-x3^4*x2^2-4*y3*y1^2*x2*x1*y2-x1^4*x3^2-4*x3^2*y3*x2*x1*y2-x1^4*x2^2+2*x3*x1^3*y3^2-2*x3^3*x1^2*x2-2*x3^3*x1*x2^2+2*x3^3*x1*y2^2+2*y1^2*x3^3*x2-2*x3^2*x1^2*y3^2+2*x3^4*y2*y1-2*x3^2*y3^2*x2^2-2*x3^2*x1^2*y2^2-2*x3^2*y1^2*x2^2-2*y2^2*y1^2*x3^2+2*y2*y1^3*x3^2+2*y1^3*y3*x3^2-2*y1^2*y3^2*x3^2-2*y3^2*y2^2*x3^2+2*y2^3*y1*x3^2+2*y3*y2^3*x3^2-4*x3*y2^3*y1*x1+2*x3*y3^2*y2^2*x2+2*x3*y2^2*y1^2*x2+4*x3^2*y3^2*x2*x1+2*x3^2*y3*x2^2*y1+2*x3^2*x1^2*y2*y3-4*x3^3*y2*y1*x2-4*x3^3*x1*y2*y1+2*x2^2*y1*x3^2*y2+2*x1^2*y3*y1*x3^2-2*y1^2*y3*x3^2*y2+4*y1*y3^2*x3^2*y2+2*y3*x2^2*x3^2*y2-2*y3*y2^2*y1*x3^2+2*y2*x1^2*y1*x3^2+2*x3*y2^2*y1^2*x1-4*x3*y2*y1^3*x2-4*x3*x2^3*y1*y3-2*x3*x1^2*y3^2*x2-4*x3*x1^3*y3*y2+2*x3*y1^2*y3^2*x2+2*x3*y1^2*y3^2*x1-4*x3*y1^3*y3*x2-y2^2*y1^4-x3^4*y1^2-4*x3*y3*y2^3*x1+4*y2*y1^2*x1^2*y3-2*y2*y1^2*y3*x2^2+2*x2^2*y1*x1^2*y3-2*x2^2*y1*y3^2*y2+4*x2^2*y1*y3*y2^2+2*x2^2*y1*y2*x1^2-2*x1^2*y3*y2^2*y1-2*y1*y3^2*y2*x1^2+2*y3*x2^2*y2*x1^2-4*y3^3*x2*x1*y2-4*y3^3*x1*y1*x2+8*x3*y2*y1^2*y3*x2-4*x3*y2*y1^2*x1*y3-4*x3*x2^2*y1*x1*y2+8*x3*x2^2*y1*x1*y3-4*x3*x1^2*y3*y1*x2-4*x3*y1*y3^2*x1*y2-4*x3*y3*x2^2*x1*y2-4*x3*y3^2*y2*y1*x2-4*x3*y2^2*y1*y3*x2+8*x3*y2^2*y1*x1*y3+8*x3*y2*x1^2*y3*x2-4*x3*y2*x1^2*y1*x2+2*y2*y1^3*x2^2+2*y2*y1^4*y3-2*y2*y1^3*y3^2+6*y2^2*y1^2*y3^2-2*y2^3*y1^2*y3-2*y2^2*y1^2*x1^2-x3^2*y2^4+2*x3*y3^2*y2^2*x1+2*x3*x2^3*y1^2, label = _L6)/(x3*y2-y3*x2-x1*y2+x1*y3+y1*x2-y1*x3)}