\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Determine whether \(\{x + y + z = 1 \;;\; 2 x + 2 y + z = 3 \;;\; 3 x + 3 y + 2 z = 5\}\) is compatible. If yes, solve it; if no, exhibit the incompatibility.
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