System 3

Algebra Level 5

\[\large\begin{cases} x^2+y^2+xy+2y+x=2 \\ 2x^2-y^2-2y-2=0\end{cases}\] If \((x,y)=(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)\) are all real pairs satisfying the system above, find \(\left|\displaystyle\sum _{m=1}^{n} x_m+y_m\right|\) to 2 decimal places.

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