Systems of Inequalities Review

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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 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 graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.

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

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A point is a solution to a system of inequalities if it satisfies all inequalities in the system.

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What is the significance of the boundary line in a linear inequality?

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The boundary line represents the points where the inequality changes from true to false. Points on the line are included if the inequality is ≤ or ≥.

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How can you determine if a point is a solution to a system of inequalities?

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Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the graphical representation of the solution set for a system of inequalities?

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The solution set is represented by the shaded region where all inequalities overlap on the graph.

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What does the term 'feasible region' refer to in the context of systems of inequalities?

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The feasible region is the area on the graph that represents all possible solutions to the system of inequalities.

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How do you write a system of inequalities from a word problem?

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

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

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How do you find the intersection of two inequalities?

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Graph both inequalities and identify the region where they overlap. This overlapping region represents the intersection.