No Solution (Systems of Equations)
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
No solution refers to a situation where a system of linear equations has no points of intersection, meaning the two lines in the system are parallel and never meet.
Explanation:
When two lines are parallel, they have the same slope but different y-intercepts.
Since the lines never intersect, there are no points that satisfy both equations simultaneously.
Thus, the system has no solution.
Conditions for No Solution:
The two equations must have the same slope but different y-intercepts.
Example:
Consider the system of equations:
y = 2x + 3
y = 2x - 1
Both lines have the same slope (m = 2), but different y-intercepts (3 and -1). Graphing these equations, you would see two parallel lines that never intersect. Therefore, the system has no solution.
Graphically:
If you graph both equations, the lines will be parallel to each other, meaning they will never cross, and there is no common point that satisfies both equations. This is why the system has no solution.