Systems of Inequalities

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What is a system of inequalities?

Back

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. Use a dashed line for 'greater than' or 'less than' and a solid line for 'greater than or equal to' or 'less than or equal to'. Then, shade the appropriate region for each inequality.

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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 inequalities in the system, meaning it lies in the shaded region of the graph.

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What is the difference between 'greater than' and 'greater than or equal to'?

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'Greater than' (>) means that the value is not included in the solution, while 'greater than or equal to' (≥) includes the boundary line in the solution.

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What is the difference between 'less than' and 'less than or equal to'?

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'Less than' (<) means that the value is not included in the solution, while 'less than or equal to' (≤) includes the boundary line in the solution.

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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 does the shaded region in a graph of a system of inequalities represent?

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The shaded region represents all possible solutions to the system of inequalities.

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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. Whether the line is included in the solution depends on whether the inequality is strict or inclusive.

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How do you identify a point that is NOT a solution to a system of inequalities?

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A point that does not satisfy at least one of the inequalities in the system is NOT a solution.

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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 + 3.