When is a system inconsistent?
When it has no solution.
A system is inconsistent when it cannot have a solution that satisfies all of its equations or constraints simultaneously. In other words, there are conflicting requirements or conditions that cannot be met by any single solution. For example, if we have two equations in two variables, and they contradict each other, then the system is inconsistent. Another example of an inconsistent system is when we have more unknown variables than equations or more equations than unknown variables, and the equations cannot be manipulated to find a single unique solution for all variables. It is important to recognize inconsistent systems because they cannot be solved using traditional methods, and they may require specialized techniques or modifications to find a solution.
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