Systems of Inequalities

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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 point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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What does a solid line represent in a graph of an inequality?

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A solid line indicates that the points on the line are included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

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What does a dashed line represent in a graph of an inequality?

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A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is 'greater than' (>) or 'less than' (<).

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What is the solution set of a system of inequalities?

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The solution set is the region where the shaded areas of all inequalities overlap on the graph.

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What is the significance of the intersection of two inequalities?

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The intersection represents the set of points that satisfy both inequalities simultaneously, forming the solution to the system.

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How can you identify the correct graph for a system of inequalities?

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To identify the correct graph, check which regions are shaded according to the inequalities and ensure the lines are solid or dashed as appropriate.

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