System of equations

Algebra Level pending

Given this system of equations (x and y are real numbers):

\(x^3-3x^2-9x+22=y^3+3y^2-9y \\ x^2+y^2-x+y=1/2\)

Let \((x_1, y_1), (x_2,y_2), ..., (x_n, y_n)\) be the solution set of the above system

Find \(n+\sum _{ i=0 }^{ n }{ (x_i + y_i) } \)

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