Well, honey, an inconsistent person is like a human mood ring - you never know what color they're gonna be next. So yeah, they probably have opinions that change more often than a Kardashian changes outfits. Mutable opinions? Sure, if by "mutable" you mean as reliable as a $5 umbrella in a windstorm.
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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).
It depends on the equations.
If you refer to linear equations, graphed as straight lines, two inconsistent equations would result in two parallel lines.
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.