Graph linear inequalities and systems of linear inequalities as half-plane solution regions.
Check whether a point is in a solution region
Problem
Determine whether \((2,3)\) lies in the solution region for \(y~\ge~x\), \(x~+~y~\le~6\).
Big Picture
What this problem is really about
A point belongs to a system’s solution region only if it satisfies every constraint at once. We’ll substitute its coordinates into each inequality separately, preserve the ordered-pair roles, and evaluate every comparison. One false statement is enough to exclude the point, while membership follows only after all required tests are true.
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