Is it possible for a system of linear equations to have exactly two solutions?

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Solution

Explanation:
No. A consistent system is either dependent (both equations represent the same line) or independent.
So in an independent system, the lines intersect in exactly one point, which means there is exactly one solution.
A dependent system has an infinite number of solutions.
An inconsistent system has no solution, so no system of linear equations can have exactly two solutions.
Hence, a system of linear equations in two variables may have zero, one, or infinitely many solutions.

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