5.6 Systems of Inequalities Practice

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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 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 does it mean if a point is not a solution to a system of inequalities?

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If a point is not a solution, it means that when the coordinates are substituted into the inequalities, at least one inequality is not satisfied.

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What is the graphical representation of a system of inequalities?

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The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of each inequality.

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

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The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or equal to the number.

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

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The symbol '>' means 'greater than', indicating that the value must be strictly greater than the number.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality.

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

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

Front

What is a feasible region in the context of systems of inequalities?

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The feasible region is the area on the graph where all shaded regions overlap, representing all possible solutions to the system of inequalities.

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How can you identify a solution from a graph of a system of inequalities?

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A solution can be identified as any point within the feasible region of the graph.