These roots have roots

Algebra Level 5

Find the number of ordered pairs of real numbers (x,y) (x,y) such that

{x=y+1000y+100y=x+1000x+100. \begin{cases} x = \sqrt{y+1000} - \sqrt{y+100} \\ y = \sqrt{x+ 1000 } - \sqrt{ x +100} .\\ \end{cases}

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