Q2 Benchmark Topic 2: Systems of Inequalities Exit Ticket

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What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all ordered pairs 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. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution set is where the shaded regions overlap.

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What does the solution set of a system of inequalities represent?

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

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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 indicates the limits of the solution set. If the inequality is strict (< or >), the line is dashed; if it is inclusive (≤ or ≥), the line is solid.

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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 is the meaning of 'x + y ≤ 300' in a real-world context?

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This inequality means that the total number of two types of items (x and y) cannot exceed 300. For example, it could represent the maximum number of tickets sold in a theater.

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What does '7.5x + 5.5y ≥ 2000' represent in a ticket sales scenario?

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This inequality indicates that the total revenue from selling x adult tickets at $7.50 each and y children's tickets at $5.50 each must be at least $2000.

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What is the difference between '≤' and '<' in inequalities?

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'≤' means 'less than or equal to', including the boundary, while '<' means 'less than', excluding the boundary.

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How can you represent a situation with two variables using inequalities?

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You can represent a situation with two variables by identifying constraints and relationships between the variables, then writing inequalities that reflect those conditions.

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What does the inequality 'x + y < 10' signify in a basketball challenge?

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This inequality signifies that the total number of shots taken (x for 2-point shots and y for 3-point shots) must be less than 10.