Q2 Benchmark Topic 2: Systems of Inequalities Exit Ticket

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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 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 region that satisfies the inequality. The solution set is where the shaded regions overlap.

Tags

CCSS.HSA.REI.D.12

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

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The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Tags

CCSS.6.EE.B.8

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

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The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Tags

CCSS.6.EE.B.8

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How can 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 point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the significance of the boundary line in a graph of an inequality?

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The boundary line represents the values where the inequality changes from true to false. If the inequality is strict (e.g., < or >), the line is dashed; if it includes equality (≤ or ≥), the line is solid.

Tags

CCSS.HSA.REI.D.12

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What is the solution set of a system of inequalities?

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The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

Tags

CCSS.HSA.REI.D.12

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How do you solve a word problem involving a system of inequalities?

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Identify the variables, write inequalities based on the problem's constraints, and then graph the inequalities to find the feasible region.

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

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A feasible solution is one that satisfies all constraints of the system, meaning it lies within the solution set.

Tags

CCSS.HSA.REI.D.12

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What is an example of a real-world application of systems of inequalities?

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An example is budgeting for purchases, where the total cost must not exceed a certain amount while considering the prices of different items.