Systems of Linear Inequalities

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What is a system of linear inequalities?

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A system of linear 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 '≤' represent in linear inequalities?

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The symbol '≤' means 'less than or equal to'. It indicates that the values can be equal to the boundary line or less than it.

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What does the symbol '≥' represent in linear inequalities?

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The symbol '≥' means 'greater than or equal to'. It indicates that the values can be equal to the boundary line or greater than it.

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When graphing an inequality, what type of line is used for '>' or '<'?

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A dotted line is used when graphing inequalities with '>' or '<' to indicate that points on the line are not included in the solution.

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When graphing an inequality, what type of line is used for '≥' or '≤'?

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A solid line is used when graphing inequalities with '≥' or '≤' to indicate that points on the line are included in the solution.

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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 it mean if a point lies on the boundary line of an inequality?

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If a point lies on the boundary line of an inequality, it may or may not be included in the solution set, depending on whether the inequality is strict ('<' or '>') or inclusive ('≤' or '≥').

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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 solutions that satisfy both inequalities simultaneously.