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 symbol '≥' indicate in an inequality?

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The symbol '≥' means 'greater than or equal to'. It indicates that the value can be greater than or equal to a certain number.

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

Back

The symbol '<' means 'less than'. It indicates that the value must be smaller than a certain number.

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

Back

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

Front

How do you graph the inequality @@y ge 3x + 2@@?

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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 the inequalities in the system, meaning it lies in the overlapping shaded region.

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Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the graphical representation of the inequality @@y ge 2x - 1@@?

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

Back

The symbol '>' means 'greater than'. It indicates that the value must be larger than a certain number.