Systemsme syndicate

Algebra Level 5

\[\large \left\{\begin{matrix} 4y^3-(4x+29)\sqrt{x+7}+y=0 & & \\ y^3+3x^2-y^2\sqrt{x+7}+6x-\frac{y}{\sqrt{3}}=3 & & \end{matrix}\right.\]

How many pairs of \((x,y)\) satisfy the system of equations above?

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