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No. There are none, one or infinitely many solutions. No other value is possible.

A system of two linear equation can be represented by two straight lines in space (of 2 or more dimensions).

Such lines can be non-intersecting (0 solutions),

or they can intersect at one point (1 solution),

or they can be coincident (infinitely many solns).

Two non-intersecting lines in 2-d space must be parallel but in spaces of 3 or more dimensions they can simply be non-coplanar. For example, imagine you are in a cuboid room. One line is the join of the walls to your left and behind you, the other line is where the floor meets the far wall. These lines are not parallel but they do not meet.

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