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 linear 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 solid if the inequality is '≤' or '≥', and dashed if it is '<' or '>'.

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What does it mean if a system of inequalities has no solution?

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A system of inequalities has no solution if the regions represented by the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

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What does it mean if a system of inequalities has infinitely many solutions?

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A system of inequalities has infinitely many solutions if the regions represented by the inequalities overlap in such a way that there are countless points that satisfy all inequalities.

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When do you use a solid line when graphing inequalities?

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You use a solid line when graphing inequalities with '≤' or '≥', indicating that points on the line are included in the solution set.

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When do you use a dashed line when graphing inequalities?

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You use a dashed line when graphing inequalities with '<' or '>', indicating that points on the line are not included in the solution set.

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How do you determine the feasible region in a system of inequalities?

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The feasible region is determined by graphing all inequalities and identifying the area where all shaded regions overlap.

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What is the significance of the vertices in the feasible region?

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The vertices of the feasible region are significant because they represent potential solutions to the system of inequalities, often used in optimization problems.

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How can you solve a system of inequalities algebraically?

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To solve a system of inequalities algebraically, you can isolate variables and find the range of values that satisfy all inequalities.

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