Coincident Lines
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
Coincident lines refer to two lines that lie exactly on top of each other, meaning they have the same slope and the same y-intercept. In other words, they are essentially the same line, even though they might be represented by two different equations.
When you solve a system of linear equations and you find that the two equations represent coincident lines, this means there are infinitely many solutions, since every point on one line is also on the other line.
In a graphical sense, coincident lines look like one single line that appears twice because the equations describe the same relationship between x and y.
Example:
Consider the system of equations:
1. y = 2x + 3
2. y = 2x + 3
These two equations describe the same line, so the lines are coincident. In this case, there are infinitely many solutions because every point on the line is a solution to both equations.