Correct. Unless the parallel lines are coincident, in which case the solution set is the whole line.
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No Solutions
There will be o solutions.
NO! A linear system can only have one solution (the lines intersect at one point), no solution (the lines are parallel), and infinitely many solutions (the lines are equivalent).
The set of points the graphed equations have in common. This is usually a single point but the lines can be coincident in which case the solution is a line or they can be parallel in which case there are no solutions to represent.
Parallel