Graphing Systems of Inequalities A1PB

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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How do you determine if a point is a solution to a system of inequalities?

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To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What does the shaded region in a graph of inequalities represent?

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The shaded region represents all the possible solutions to the system of inequalities.

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What is the significance of the boundary line in a graph of inequalities?

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The boundary line indicates the limits of the solution set. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution set (inclusive inequality), while a dashed line indicates that points on the line are not included (strict inequality).

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What does it mean if a point lies in the intersection of two shaded regions?

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If a point lies in the intersection of two shaded regions, it satisfies both inequalities and is a solution to the system.

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What is the first step in solving a system of inequalities by graphing?

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The first step is to graph each inequality on the same coordinate plane.

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What is a feasible region in the context of systems of inequalities?

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The feasible region is the area on the graph where all the shaded regions overlap, representing all possible solutions to the system.