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I have a system of quadratic equations of two variables to solve in several moduli:

$z_0 \equiv (x+k_0)^2-(x+k_0)y \ (mod\ n_0)$
$z_1 \equiv (x+k_1)^2-(x+k_1)y \ (mod\ n_1)$
...
a $z_m \equiv (x+k_m)^2-(x+k_m)y \ (mod\ n_m)$

I know the values of all the $z_i$, $k_i$, and $n_i$ $\forall i$, and I wish to solve for $x$ and $y$. All $n$s are co-prime if that helps.

Can I solve a system of equations like this faster than exhaustively searching?

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