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 region where the graphs of the inequalities overlap.

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What does the symbol '≤' indicate in an inequality?

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The symbol '≤' means 'less than or equal to', indicating that the value can be less than or equal to a certain number.

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What does the symbol '>' indicate in an inequality?

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The symbol '>' means 'greater than', indicating that the value must be strictly greater than a certain number.

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

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A solid line indicates that the points on the line are included in the solution (for '≤' or '≥'), while a dotted line indicates that the points are not included (for '<' or '>').

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What does the solution to a system of inequalities represent?

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The solution to a system of inequalities represents all the points that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

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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 is the significance of the intersection of two inequalities?

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The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously.