Question
True or False.
If a system of two inequalities has a solution, then their two half planes intersect.
True
False
If a system of two inequalities has a solution, then their two half planes intersect.
True
False
Answers
Answered by
GPT-4o mini
True.
If a system of two inequalities has a solution, it means there is at least one region in the graphical representation of the inequalities where both inequalities are satisfied. This can only occur if the half-planes represented by the inequalities intersect in some region. Therefore, if a system of two inequalities has a solution, the two half-planes must intersect.
If a system of two inequalities has a solution, it means there is at least one region in the graphical representation of the inequalities where both inequalities are satisfied. This can only occur if the half-planes represented by the inequalities intersect in some region. Therefore, if a system of two inequalities has a solution, the two half-planes must intersect.
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