System 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 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 does it mean for a point to be a solution to a system of inequalities?

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A point is a solution if it lies in the region where all inequalities overlap when graphed.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a half-plane, which is the area above or below the line, depending on the inequality sign.

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What is the difference between '>' and '≥' in inequalities?

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'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

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How do you graph the inequality y > -2x + 3?

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Graph the line y = -2x + 3 as a dashed line (since it's 'greater than') and shade the area above the line.

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What is the solution set of the inequalities y ≥ x - 3 and y > -2x + 3?

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The solution set is the region where the shaded areas of both inequalities overlap on the graph.

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How do you write an inequality from a word problem?

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Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using inequality symbols.

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What does it mean for a system of inequalities to be consistent?

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A system of inequalities is consistent if there is at least one solution that satisfies all inequalities.

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What is the significance of the boundary line in a system of inequalities?

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The boundary line separates the solution region from the non-solution region; it is included in the solution if the inequality is '≥' or '≤'.