Graph linear inequalities and systems of linear inequalities as half-plane solution regions.
Decide whether a boundary point is included
Problem
Test boundary point \((2,5)\) for \(C_{1}\): \(y\le~2x+1\).
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What this problem is really about
A point on a boundary is not automatically included or excluded. We’ll substitute both coordinates into the named constraint, compare the two sides exactly, and then inspect whether the inequality symbol permits equality. That final symbol check decides whether a true equality places the point inside the solution region.
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