Any system of linear equations can have the following number of solutions:
0 if the system is inconsistent (one of the equations degenerates to 0=1)
1 if the system is linearly independent
infinity if the system has free variables and is not inconsistent.
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No. A pair of linear equation can have 0 solutions (they are parallel), or one solution (they cross at one point) or an infinite number of solutions (they represent the same line).
Yes.
No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.
All supplementary angles do not form a linear pair. The opposite angles of any quadrilateral inscribed in a circle (a cyclic quadrilateral) are supplementary but they are not a linear pair. However, all linear pair are supplementary.
Always. Every ordered pair is the solution to infinitely many equations.