2-6 Systems of Inequalities Word Problems

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What is a system of inequalities?

Back

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 situation with inequalities?

Back

You identify the constraints and conditions of the problem, then translate them into mathematical inequalities using variables.

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What does the inequality x + y < 10 represent in a word problem?

Back

It indicates that the total number of items represented by x and y must be less than 10.

Front

What does the inequality 2x + 3y ≥ 20 represent?

Back

It indicates that the total score from 2-point shots (x) and 3-point shots (y) must be at least 20 points.

Front

How do you solve a system of inequalities graphically?

Back

You graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

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What is the significance of the solution to a system of inequalities?

Back

The solution represents all possible combinations of the variables that satisfy all inequalities in the system.

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What does it mean if a solution is not included in the solution set of an inequality?

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It means that the solution does not satisfy the inequality, often indicated by a strict inequality (e.g., < or >) rather than inclusive (e.g., ≤ or ≥).

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How can you check 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 difference between a strict inequality and a non-strict inequality?

Back

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

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What is a feasible region in the context of inequalities?

Back

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