Q: Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?

A: Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?
"Do solutions to systems of linear inequalities need to satisfy both inequalities?"
YES. Absolutely. [ Solving a system of linear inequalities MEANS finding solutions that satisfy both inequalities. This does not mean however that there will always be solutions that can satisfy both

inequalities. In that case we state that system has no solutions.
So even when there are no solutions that satisfy both inequalities, we cannot say the solution to the system of linear equalities does not satisfy both inequalities, since system has no solution to start with.
"In what case might they not?"
Well, since solutions must satisfy both inequalities, then there are no cases where they might not. However, perhaps a more interesting question is when does a system have no solutions? When the lines defined by the inequalities are parallel and the respective solutions to the 2 inequalities are in opposite directions away from each other.
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Expert answered|hellphoenix|Points 11|

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