Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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If two lines are parallel, what is true about their solutions?

  1. They intersect at exactly one point

  2. They have infinitely many solutions

  3. They have no solutions

  4. They cross at two points

The correct answer is: They have no solutions

When two lines are parallel, they do not intersect at any point. This characteristic is fundamental to the definition of parallel lines; they maintain a constant distance from each other and will never meet. As a result, there are no points that satisfy both equations simultaneously, leading to the conclusion that the system has no solutions. This can also be understood geometrically: if you were to graph the two lines, you would see that they run alongside each other without touching, confirming that their solution set is empty.

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