Systems of Inequalities

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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 graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the region that satisfies the inequality.

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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 satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

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

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The boundary line represents the points where the inequality changes from true to false. It helps determine the regions to shade for solutions.

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How can 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 the symbol '≥' mean in an inequality?

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The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to a certain number.

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What does the symbol '<' mean in an inequality?

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The symbol '<' means 'less than', indicating that the value must be strictly less than a certain number.

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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, often represented as a shaded region on a graph.

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How do you identify a point that is not a solution to a system of inequalities?

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A point that does not satisfy at least one inequality in the system is identified as not a solution, meaning it lies outside the shaded region.