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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 linear 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 if a system of linear inequalities has no solution?

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A system has no solution if there is no point that satisfies all inequalities, often represented by parallel lines that do not intersect.

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What does it mean if a system of linear inequalities has infinitely many solutions?

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A system has infinitely many solutions if the inequalities overlap in such a way that there are countless points that satisfy all inequalities, often forming a region.

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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 divided by a boundary line, where one side of the line represents the solutions.

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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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To identify a non-solution, substitute each point into the inequalities. The point that fails to satisfy at least one inequality is the non-solution.

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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 if the inequality is 'less than or equal to' or 'greater than or equal to'.

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What does the term 'feasible region' refer to in linear inequalities?

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The feasible region is the area on a graph where all the solutions to the system of inequalities lie. It is the intersection of all half-planes.

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What is the role of test points in solving systems of inequalities?

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Test points are used to determine which side of the boundary line satisfies the inequality. If the test point satisfies the inequality, that side is part of the solution.