Zero; they never intersect and therefore they do not have a solution.
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Nope; they don't intersect.
A triangle can have no parallel lines.
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
A pentagon has no parallel lines.
A cube has exactly 6 parallel lines.