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Solve, for \(p \in \mathbb{R}\), the system \(\{2 p x + y = p \;;\; 2 x + p y = p\}\) in \((x, y) \in \mathbb{R}^2\). Treat the value \(p = 0\) first (no row operation is needed), then for \(p \ne 0\) apply Gauss and discuss the remaining cases.
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