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 with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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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 the symbol '≥' mean in an inequality?

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'≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Tags

CCSS.6.EE.B.8

Front

What does the symbol '≤' mean in an inequality?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

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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 half-plane divided by a line. The line is solid if the inequality includes equality (≥ or ≤) and dashed if it does not (> or <).

Tags

CCSS.HSA.REI.D.12

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What is the feasible region in a system of inequalities?

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

Tags

CCSS.HSA.REI.D.12

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How can you represent a real-world situation using a system of inequalities?

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You can represent a real-world situation by defining variables for the quantities involved, then writing inequalities based on the constraints of the situation.

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What is the difference between 'strict' and 'non-strict' inequalities?

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Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line.

Tags

CCSS.HSA.REI.D.12

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If a point lies on the boundary line of an inequality, is it a solution?

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Yes, if the inequality is non-strict (≤ or ≥), the point on the boundary line is considered a solution.

Tags

CCSS.HSA.REI.D.12

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What is the significance of the slope in a linear inequality?

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The slope indicates the steepness of the line and the direction of the inequality. A positive slope means the line rises, while a negative slope means it falls.