Get the value $x+y$

Number Theory Level 2

$\begin{aligned} x^3 + y^2 + x^2 y + xy & = & 91 \\ x^4 + 2x^2 y + y^2 &= & 169 \\ \end{aligned}$

If positive integers $x,y$ satisfy the system of equations above, what is the value of $x+y$ ?

Get the value x+yx+yx+y