Interpreting Solutions of 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 that share the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.

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How do you determine if an ordered pair is a solution to a system of inequalities?

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To determine if an ordered pair is a solution, substitute the values of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

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What does it mean for a point to be a solution of a system of inequalities?

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A point is a solution of a system of inequalities if it lies in the region where all inequalities overlap on a graph.

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What is the graphical representation of a system of inequalities?

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The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of each inequality.

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What is the significance of the boundary lines in a system of inequalities?

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Boundary lines represent the limits of the inequalities. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

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What does it mean if a point lies on a dashed line in a graph of inequalities?

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If a point lies on a dashed line, it means that the point is not included in the solution set for that inequality.

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What does it mean if a point lies on a solid line in a graph of inequalities?

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If a point lies on a solid line, it means that the point is included in the solution set for that inequality.

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How can you find the solution set of a system of inequalities?

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To find the solution set, graph each inequality, shade the appropriate regions, and identify the overlapping shaded area.

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What is an ordered pair?

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An ordered pair is a pair of numbers used to represent a point in a two-dimensional space, written in the form (x, y).

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What is the difference between a solution and a non-solution in the context of inequalities?

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A solution satisfies all inequalities in the system, while a non-solution does not satisfy at least one inequality.