# Complicated System of Equations

Algebra Level 5

Consider the distinct complex solutions $$(x_1,y_1),...,(x_n,y_n)$$ to the following system of equations: $\begin{cases} x^3+y^2+y=1\\ x^2+y^3=2. \end{cases}$ Find the absolute value of the product of all the possible $$x$$ values, i.e. $$\left| x_1\cdot x_2\cdot...\cdot x_n \right| .$$

Details and assumptions

The absolute value of a complex number $$z = a+ bi$$ is given by $$|z| = \sqrt{a^2+b^2}$$.

Due to the restriction of distinct solutions, repeated roots (if they exist) do not contribute to the product. For example, if your roots are $$(2, 3), (2, 3)$$ then the answer is 2. If your roots are $$(2, 3), (2, -3)$$ then the answer is 4.

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