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 inequality x + y ≤ 6 represent in a real-world context?

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This inequality represents a constraint where the total number of items x and y cannot exceed 6, such as hours spent on two activities.

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What is the significance of the inequality 32x + 20y ≥ 150 in a baking scenario?

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This inequality indicates that the total number of cookies baked (32 cookies per hour for x hours and 20 cookies per hour for y hours) must be at least 150.

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

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The feasible region is the area on a graph where all the inequalities in the system overlap, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

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How can you graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation, then shade the appropriate region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

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What is the difference between a solution and a feasible solution in a system of inequalities?

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A solution is any point that satisfies all inequalities, while a feasible solution is a solution that also meets all constraints of the problem.

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What does it mean if a point lies on the boundary line of an inequality?

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If a point lies on the boundary line, it satisfies the equation of the line but may or may not satisfy the inequality, depending on whether the inequality is strict or inclusive.

Tags

CCSS.HSA.REI.D.12

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What is the role of the maximum hours constraint in a real-world problem involving inequalities?

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The maximum hours constraint limits the total time available for activities, helping to define the feasible region for solutions.

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How do you interpret the solution (1, 0) in a system of inequalities?

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The solution (1, 0) means that one unit of activity x and zero units of activity y satisfy all inequalities in the system.

Tags

CCSS.8.EE.C.8B