Graphing Systems of Inequalities Review

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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 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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What does the symbol '>' represent in inequalities?

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

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What does the symbol '<' represent in inequalities?

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The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

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What does the symbol '≥' represent in inequalities?

Back

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

Front

What does the symbol '≤' represent in inequalities?

Back

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

Front

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 region that satisfies the inequality.

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What is the feasible region in a system of inequalities?

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

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What is the significance of the boundary line in graphing inequalities?

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The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. The line itself is included if the inequality is '≤' or '≥'.

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How can you find the intersection of two inequalities?

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To find the intersection, graph both inequalities and identify the region where they overlap. This overlapping region represents the solutions to both inequalities.