5.5 System 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 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 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 for an inequality to be represented by a solid line on a graph?

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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 it mean for an inequality to be represented by a dashed line on a graph?

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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 graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a shaded region on one side of the line, indicating all the solutions that satisfy the inequality.

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How can you express a real-world scenario as a system of inequalities?

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Identify the constraints and objectives in the scenario, then translate them into inequalities using variables to represent the quantities involved.

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What is the significance of the feasible region in a system of linear inequalities?

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The feasible region is the area on the graph where all the inequalities overlap, representing all possible solutions to the system.

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What does the term 'solution set' refer to in the context of linear inequalities?

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The solution set refers to all the points (x, y) that satisfy all inequalities in the system.

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How do you find the vertices of the feasible region?

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To find the vertices, graph the inequalities, identify the intersection points of the boundary lines, and determine the coordinates of these points.

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What is the role of the boundary line in a system of inequalities?

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The boundary line separates the graph into two half-planes, one of which contains the solutions to the inequality.