Graphing Systems of Inequalities

Front

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

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What does it mean for a region to be a solution set in graphing inequalities?

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The solution set is the region on the graph where all points satisfy the inequalities in the system. It is typically shaded to indicate all possible solutions.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, representing inequalities that are 'less than' or 'greater than' but not 'less than or equal to' or 'greater than or equal to'.

Front

What does a solid line represent in graphing inequalities?

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A solid line indicates that the points on the line are included in the solution set, representing inequalities that are 'less than or equal to' or 'greater than or equal to'.

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How do you graph the inequality @@y eq rac{1}{2}x + 2@@?

Back

Front

What is the first step in solving a system of inequalities by graphing?

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The first step is to graph each inequality on the same coordinate plane, using solid or dashed lines as appropriate.

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What does the term 'feasible region' refer to in the context of systems of inequalities?

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

Front

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

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The solution set can be identified by looking for the region where the shaded areas of all inequalities intersect.

Front

What is the role of test points in solving systems of inequalities?

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Test points are used to determine which side of the boundary line to shade. By substituting a test point into the inequality, you can see if it satisfies the inequality.