\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Two planes in \(\mathbb{R}^3\) --- determine whether they are secant, confounded, or parallel-distinct, and conclude geometrically. Solve and interpret: \(\{x + y - z = 2 \;;\; 2 x + 2 y - 2 z = 5\}\) in \((x, y, z) \in \mathbb{R}^3\).
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