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Determine, for \((a, b) \in \mathbb{R}^2\), the number of solutions of the system \(\{x + y + z = 1 \;;\; x + a y + z = b \;;\; x + y + a z = b\}\) in \((x, y, z) \in \mathbb{R}^3\). Identify the values of \((a, b)\) for which the system is Cramer, compatible-not-Cramer, or incompatible.
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