$2ab=6(a+b)-13$$a^2+b^2=4$ =>$(a+b)^2=6(a+b)-9$ <=>$a+b=3$ =>$2ab=6*3-13=5$ =>$(a-b)^2=(a+b)^2-4ab=9-10=-1$(nonsense) => system of equations has not solutions in set of real numbers.