Solving Systems of Inequalities Word Problems

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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 that share 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 represent the maximum capacity of a theater with inequalities?

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This inequality represents the requirement that the total revenue from ticket sales must be at least $2000.

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What type of line is used to represent inequalities with symbols < or >?

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A dotted line is used to represent inequalities with the symbols < or >.

Front

What type of line is used to represent inequalities with symbols ≤ or ≥?

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A solid line is used to represent inequalities with the symbols ≤ or ≥.

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If Homer sold 21 tickets for a total of $104, how can we express this situation with equations?

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What is the significance of the coefficients in a system of inequalities?

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The coefficients represent the cost or contribution of each variable to the total, such as ticket prices or plant costs.

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How can you determine if a combination of items is within a budget using inequalities?

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What does the solution to a system of inequalities represent graphically?

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The solution represents the region on a graph where all inequalities overlap, indicating all possible combinations that satisfy the conditions.

Front

How do you solve a system of inequalities graphically?

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Graph each inequality on the same coordinate plane and identify the overlapping region that satisfies all inequalities.