Graph linear inequalities and systems of linear inequalities as half-plane solution regions.
Graph a system of two linear inequalities
Problem
For \(y\ge~x+1\) and \(y\le~5\), identify both boundary styles, shading directions, region type, and boundary intersection.
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What this problem is really about
A system graph keeps only points satisfying both inequalities at once. We’ll construct each boundary separately, use each inclusive symbol to set its style, and identify the required half-plane for each condition. Their overlap gives the system region; solving the boundary equations together locates its corner, while tracing the overlap beyond that corner tells whether the region closes or remains unbounded.
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