inconsistent system
A system that has no solution.
An inconsistent system is a system of equations (or inequalities) that does not have any solution. In other words, it is impossible to find any values for the variables in the system that make all of the equations true simultaneously.
For example, consider the following system of linear equations:
2x + 3y = 10
4x + 6y = 5
If we try to solve this system using any of the usual methods (substitution, elimination, or matrix methods), we end up with the equation 0 = -5 which is false. This means that there are no values of x and y that make both of these equations true at the same time. Therefore, this system is inconsistent.
Geometrically, an inconsistent system of equations represents two or more lines that do not intersect at any point in the coordinate plane. Instead, they are parallel and never meet.
More Answers:
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Independent System of Linear Equations: Determinant and Unique Solutions