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

Consider the system, a₁x + b₁y + c₁z = d₁, a₂x + b₂y + c₂z = d₂of two equations in three unknowns.

(a) Use the fact that the graph of each such equation is a plane in xyz-space to explain why such a system always has either no solution or infinitely many solutions.

(b) Explain why the system must have infinitely many solutions if d₁ = 0 = d₂.

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