How to solve this system of non-linear equations My knowledge of algebra is still insufficient to solve this problem. Any help in solving the system of equations would be greatly appreciated.
$$
xy(x+y)=30\\
x^3+y^3=35
$$

$(x+y)^3=x^3+y^3+3xy(x+y)$
$\Rightarrow (x+y)^3=35+90=125\Rightarrow (x+y)=5$
$\Rightarrow xy(x+y)=5xy=30\Rightarrow xy=6$
$(x-y)^2=(x+y)^2-4xy=25-24=1\Rightarrow (x-y)=\pm1$
case 1: $x-y=1$ and $x+y=5$ ,$\Rightarrow x=3,y=2$
case 2: $x-y=-1$ and $x+y=5$, $\Rightarrow x=2,y=3$
