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What is a system of linear inequalities?

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A system of linear inequalities is a set of two or more linear inequalities that involve 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 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 defined by the inequalities, meaning it satisfies all the conditions set by the inequalities.

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What is the graphical representation of a system of linear inequalities?

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The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

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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. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

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What does it mean if a point lies above a boundary line in a linear inequality?

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If a point lies above the boundary line of a linear inequality, it satisfies the inequality if the inequality is of the form y > mx + b.

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What does it mean if a point lies below a boundary line in a linear inequality?

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If a point lies below the boundary line of a linear inequality, it satisfies the inequality if the inequality is of the form y < mx + b.

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What is the difference between a solution and a non-solution in a system of inequalities?

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A solution satisfies all inequalities in the system, while a non-solution does not satisfy at least one inequality.

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How can you identify a non-solution from a set of points?

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A non-solution can be identified by substituting the point into the inequalities; if it fails to satisfy any of them, it is a non-solution.

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What is an example of a point that is a solution to a system of inequalities?

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For example, the point (1, 0) is a solution if it satisfies all inequalities in the system.