Graphing Systems of Linear Inequalities

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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 inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

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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 if a point is a solution to a system of inequalities?

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It means that the point lies in the region defined by the inequalities, satisfying all conditions.

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What type of line is used when graphing the inequalities with < or >?

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A dotted line is used when graphing inequalities with < or > to indicate that points on the line are not included in the solution.

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What type of line is used when graphing the inequalities with ≤ or ≥?

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A solid line is used when graphing inequalities with ≤ or ≥ to indicate that points on the line are included in the solution.

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What is the solution set of a system of linear inequalities?

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

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How do you solve a system of inequalities by graphing?

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1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region, which represents the solution.

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What does it mean if a point lies outside the shaded region of a graph of inequalities?

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It means that the point does not satisfy at least one of the inequalities in the system.

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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 and indicates whether points on the line are included based on the type of inequality.