Systems of Inequalities Word Problems

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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 points that satisfy all inequalities in the system.

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How do you represent a word problem as a system of inequalities?

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Identify the variables, determine the constraints (limits) and objectives, and translate them into inequalities based on the relationships described in the problem.

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What does the inequality x + y ≤ 6 represent in a word problem?

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It indicates that the total of two quantities, x and y, cannot exceed 6, often representing a limit on resources or time.

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What does the inequality 32x + 20y ≥ 150 represent in a word problem?

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It indicates that the total output from two activities (x and y) must meet or exceed a certain requirement, in this case, at least 150 cookies.

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What is the significance of the '≥' symbol in inequalities?

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The '≥' symbol means 'greater than or equal to,' indicating that the value can be either greater than or exactly equal to the number.

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What is the significance of the '<' symbol in inequalities?

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The '<' symbol means 'less than,' indicating that the value must be strictly less than the number.

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

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Graph each inequality on the same coordinate plane and identify the overlapping region that satisfies all inequalities.

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What does it mean if a point is in the feasible region of a system of inequalities?

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It means that the point satisfies all inequalities in the system, making it a potential solution to the problem.

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What is the first step in solving a word problem involving systems of inequalities?

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Identify the variables that represent the quantities in the problem.

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How can you check if a solution satisfies a system of inequalities?

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Substitute the solution values into each inequality and verify that all inequalities hold true.