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A System of Linear Inequalities with Parallel Boundary Lines and a Solution
A system of linear inequalities whose boundary lines are parallel can still possess a solution. While parallel lines themselves never intersect, the overall solution to a system of inequalities is determined by the overlapping of their shaded regions, not merely the intersection of their boundary lines. If the inequalities are shaded such that their respective regions overlap—which typically occurs when both inequalities mandate shading in the same general direction—the system is considered to have a solution. In these instances, one shaded half-plane is often entirely contained within the other, meaning the solution to the entire system is simply the region dictated by the more restrictive inequality. Therefore, the presence of parallel boundary lines does not automatically guarantee that the system will have no solution.
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Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
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A System of Linear Inequalities with Parallel Boundary Lines and a Solution