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

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closed as too localized by Gerry Myerson, Amzoti, Lord_Farin, Micah, Asaf Karagila May 28 '13 at 13:20

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No source, no motivation, no effort beyond cut'n'paste --- not good for this website. – Gerry Myerson May 28 '13 at 12:26
yeah same from some effort ,show steps where you've stuck. – iostream007 May 28 '13 at 12:29
up vote 3 down vote accepted

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:

enter image description here

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

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