Weird Equations

Algebra Level 5

\[\begin{align*} x^4+2y^3 - x & = -\frac{1}{4} + 3\sqrt{3} \\ y^4 + 2x^3 - y & = -\frac{1}{4} - 3\sqrt{3} \end{align*} \]

Find the number of solutions in real numbers to the system of equations above.

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