Finding the value of $x+y$ 
$x^3+y^3=(x+y)(x^2-xy+y^2)=400$
and for 
$x^2y+xy^2=(x+y)(x^2+y^2)=200$
I decided to multiply by $2$ on both sides: $(x+y)(x^2+y^2)=200$ or $2(x+y)(x^2+y^2)=2(200)$
So then I set the equations equal to each other:
$2(x+y)(x^2+y^2)=(x+y)(x^2-xy+y^2)=400$
I am having trouble solving though because there is two variables involved. Any ideas?

Hint: $(x+y)^3=x^3+3x^2y+3xy^2+y^3=x^3+y^3+3xy(x+y)$.
