Dec 06_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 region where the graphs of the inequalities overlap.

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What does it mean to shade below in a graph of an inequality?

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Shading below indicates that the solutions to the inequality are all the points below the line, meaning the y-values are less than the corresponding x-values.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

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If a system of inequalities has no solution, what does that mean?

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It means that there is no point that satisfies all inequalities in the system; the graphs do not intersect.

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How do you determine if a point is a solution to a system of inequalities?

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Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the significance of the intersection of two lines in a system of inequalities?

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The intersection represents a point that may be a solution to the system, depending on the inequalities.