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 that involve 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 represent a linear inequality graphically?

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A linear inequality is represented graphically by a region on one side of a line. The line is dashed if the inequality is strict (< or >) and solid if it is inclusive (≤ or ≥).

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

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The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

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What does the symbol '<' mean in an inequality?

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The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

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What does the symbol '≥' mean in an inequality?

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The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

Front

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

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The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

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How do you solve a system of linear inequalities by graphing?

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To solve a system of linear inequalities by graphing, graph each inequality on the same coordinate plane, identify the overlapping region that satisfies all inequalities, and that region represents the 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 solutions that satisfy both inequalities simultaneously.

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

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A feasible region is the area on a graph where all the constraints (inequalities) of a linear programming problem are satisfied.

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