An inconsistent system of equations is when you have 2 or more equations, but it is not possible to satisfy all of them at the same time. (E.g if you have 3 equations, but can only satisfy 2 at once, it is an inconsistent system).
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It is a system of linear equations which does not have a solution.
We call the coefficients of the variables in the system D, and we need to find the determinant of D. When D = 0, the system is either inconsistent or dependent. You need another method to solve it.
If you refer to linear equations, graphed as straight lines, two inconsistent equations would result in two parallel lines.
An "inconsistent" set of equations. If they are all linear equations then the matrix of coefficients is singular.
The system is inconsistent because there is no solution, i.e., no ordered pair, that satisfies both equations. You can see that this will be the case by seeing that their graphs have the same slope (2) but different y-intercepts (2 and 3/4 respectively). So the lines are parallel and will not intersect.