2.6 - 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 the slope-intercept form of a linear inequality look like?

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How do you convert a linear inequality to slope-intercept form?

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What does the symbol '>' indicate in an inequality?

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The symbol '>' indicates that the value on the left is greater than the value on the right.

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What does the symbol '≥' indicate in an inequality?

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The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. Then shade the appropriate region.

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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 is the significance of the intersection of two inequalities?

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The intersection of two inequalities represents the set of solutions that satisfy both inequalities simultaneously.