\[\large \begin{cases} x^{2}-2xy+2y^{2}-20x+5y-4=0 \\ 3x+2y+1=0 \end{cases} \]

Given that there exist two solution pairs \((x_{1},y_{1})\) and \((x_{2},y_{2})\) for the above system of equations, find \(x_{1}+y_{1}+x_{2}+y_{2}\) correct to three decimal places.

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