Question: Consider the linear system a 1 x + b 1 y + c 1 z = d 1 a 2 x + b 2 y

Consider the linear system

a₁x + b₁y + c₁z = d₁
a₂x + b₂y + c₂z = d₂
a₃x + b₃y + c₃z = d₃

of three equations in three unknowns to represent three planes P₁, P₂, and P₃ in xyz-space. Describe the solution set of the system in each of the following cases.
(a) The three planes are parallel and distinct.
(b) The three planes coincide—P₁ = P₂ = P₃.
(c) P₁ and P₂ coincide and are parallel to P₃.
(d) P₁ and P₂ intersect in a line L that is parallel to P₃.
(e) P₁ and P₂ intersect in a line L that lies in P₃.
(f) P₁ and P₂ intersect in a line L that intersects P₃ in a single point.

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