Practice question · Multiple choice
Three equations in three unknowns can have no solution even when no two of them contradict each other. How?
Hints
- Three planes, each pair meeting in a line. Ask whether those three lines must intersect.
- Picture a triangular prism and its three faces.
Show the answer
B. Because inconsistency can be a property of the three together
Why
Each pair of planes meets in a line, and the three lines can run parallel down a prism without ever sharing a point. Inconsistency is a property of the system rather than of any pair, which is why elimination is needed to detect it, checking equations two at a time will never find this.
Practise Systems of Linear Equations
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