More than a system

Algebra Level 5

\[\large\begin{cases} \sqrt{x-1}+2\sqrt{y+1}=y+\frac{9}{4} \\ \frac{x-1}{1+\sqrt{y+1}}+\frac{y+1}{1+\sqrt{x-1}}=\frac{1}{3}\end{cases}\] Give the product of all the solutions to the system above, give your answer to 4 decimal places.

Clarification: If the system has the solutions \((x_1;y_1),(x_2;y_2),\ldots \) then the product is \(x_1y_1x_2y_2 \cdots\).
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