Solve the following system of equations

Question

Solve the following system of equations: $\left\{\begin{matrix} x^3(1-x)+y^3(1-y)=12xy+18\\ \left | 3x-2y+10 \right |+\left | 2x-3y \right |=10 \end{matrix}\right.$

Answer 1

Perhaps asking Mathematica(WolframAlpha gives the answer as well) to solve it:

Solve[{x^3 (1 - x) + y^3 (1 - y) == 12 x y + 18, 
       Abs[3 x - 2 y + 10] + Abs[2 x - 3 y] == 10}, {x, y}, Reals]

immediately gives:

$$\left\{\left\{x\to -\sqrt{3},y\to \sqrt{3}\right\}\right\}$$

And there is this nice plot of the two curves:

P.S. I will probably(if I find a reason to) add an analytic answer later.