A number theory problem by Vitor Santos

\(x,y,z,t\) are all integers satisfying the following system of equations: \[ \begin{cases} \begin{align} xz-2yt&=3 \\ xt+yz&=1. \end{align} \end{cases}\] Find \( x^2+y^2+z^2+ t^2 \).

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