Solutions to Systems of Inequalities- Graphs!

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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?

Back

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?

Back

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 the shaded regions of the inequalities on a coordinate plane, where the overlapping shaded area represents the solution set.

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

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

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

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

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

Back

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

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

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

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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 appropriate region.

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What is the significance of the intersection of shaded regions in a system of inequalities?

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The intersection of shaded regions represents the set of all solutions that satisfy all inequalities in the system.