Ohio Assessments for Educators (OAE) Mathematics Practice Exam

When is it said that two lines are coincident?

1. When they have one solution

2. When they are parallel

3. When they have no solutions

4. When they lie on top of each other

The correct answer is: When they lie on top of each other

Two lines are said to be coincident when they lie on top of each other. This means that they have all their points in common, essentially representing the same line with the same slope and y-intercept. In the context of linear equations, coincident lines have an infinite number of solutions since any point on one line is also a point on the other line. This characteristic distinguishes them from other relationships between lines, such as parallel lines, which never intersect and thus have no solutions, and intersecting lines, which meet at a single point and have only one solution. Understanding this concept is fundamental in geometry and algebra, as it helps in solving systems of equations and in graphing linear functions.