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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How do you determine if a line is solid or dotted when graphing inequalities?

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A solid line is used for inequalities that include equal to (≥ or ≤), while a dotted line is used for strict inequalities (> or <).

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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. Points on one side of the line satisfy the inequality, while points on the other side do not.

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How do you graph the inequality @@y eq -rac{1}{3}x + 2@@?

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What does the symbol @@ eq@@ mean in the context of inequalities?

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The symbol @@ eq@@ means 'not equal to' and is used to indicate that a value does not satisfy the equation or inequality.

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What is the difference between a solid line and a dotted 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 dotted line indicates that points on the line are not included (> or <).

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How do you find the intersection of two inequalities?

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To find the intersection, graph both inequalities and identify the region where their shaded areas overlap.

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