6 solutions in all

Algebra Level 3

Consider the system of equations

\[ \begin{cases} -3 xy = - \frac{7}{2} \\ -x^3 - y^3 = \frac{20}{27} \\ \end{cases} \]

There are 6 solutions \( (x_i, y_i ) \) in total. If we let \( z_1=x_1+y_1=x_2+y_2 ; z_2=x_3+y_3 ; z_3=x_4+y_4 ; z_4=x_5+y_5=x_6+y_6\), then find \( (2*z_1)+z_2+z_3+(2*z_4) \)

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