Consider the system
a1x + b1y + c1z = d1
a2x + b2y + c2z = d2
of two equations in three unknowns.
(a) Use the fact that the graph of the 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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