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 set of all points that satisfy all inequalities in the system.

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How do you graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution to the system is where the shaded regions overlap.

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

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'≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

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

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'>' means 'greater than'. It indicates that the value on the left is strictly greater than the value on the right.

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What does the symbol '≤' mean in an inequality?

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'≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

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

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'<' means 'less than'. It indicates that the value on the left is strictly less than the value on the right.

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How can 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 x and y values 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 boundary line in graphing inequalities?

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The boundary line represents the values where the inequality changes from true to false. If the inequality is '≥' or '≤', the line is solid; if it is '>' or '<', the line is dashed.

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What is the solution set of a system of inequalities?

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The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

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What is an example of a system of inequalities?

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An example is: y > 2x + 1 and y ≤ -x + 4.