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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 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 does it mean for a linear inequality to be in standard form?

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A linear inequality is in standard form when it is expressed as Ax + By < C, Ax + By ≤ C, Ax + By > C, or Ax + By ≥ C, where A, B, and C are constants.

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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 region of the coordinate plane that is either shaded above or below the boundary line, depending on the inequality sign.

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

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How do you graph a system of inequalities?

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To graph a system of inequalities, graph each inequality on the same coordinate plane, shading the appropriate region for each. The solution set is where the shaded regions overlap.

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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 to a system of inequalities if it lies in the overlapping shaded region of the graph of the inequalities.

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How can you write a linear inequality from a word problem?

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Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it in the form of a linear inequality using variables.

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What is the significance of the boundary line in a linear inequality?

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The boundary line represents the points where the inequality changes from true to false. It is included in the solution for non-strict inequalities.

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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, represented graphically as the overlapping shaded region.