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.

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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.

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

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'≤' 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.

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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 can be greater than or equal to the value on the right.

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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.

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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 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 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 (>, <), the line is dashed; if it includes equality (≥, ≤), the line is solid.

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How can you express a real-world problem as a system of inequalities?

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Identify the constraints and relationships in the problem, define variables for the quantities involved, and write inequalities based on those constraints.

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What is the maximum number of items you can buy if each item has a cost and you have a budget?

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Set up an inequality where the total cost (cost per item multiplied by the number of items) is less than or equal to the budget. Solve for the number of items.

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What does it mean if a system of inequalities has no solution?

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If a system of inequalities has no solution, it means that there is no point that satisfies all inequalities simultaneously, often due to conflicting constraints.