Systems of Inequalities

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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.

Tags

CCSS.HSA.REI.D.12

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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 when substituted into them.

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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 solid line for ≤ or ≥ and a dashed line for < or >. Then shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

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

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

Tags

CCSS.HSA.REI.D.12

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What does the solution set of a system of inequalities represent?

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The solution set represents all the points that satisfy all inequalities in the system, often visualized as a shaded region on a graph.

Tags

CCSS.HSA.REI.D.12

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What is an example of a system of inequalities?

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Example: x + 2y ≥ 4 and 3x - 2y < 4.

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How can you determine if a point is a solution to a system of inequalities?

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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 it mean if a system of inequalities has no solution?

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A system has no solution if there is no point that satisfies all inequalities, often due to conflicting constraints.

Tags

CCSS.HSA.REI.D.12

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What does it mean if a system of inequalities has infinite solutions?

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A system has infinite solutions if there are multiple points that satisfy all inequalities, often represented by a shaded region.

Tags

CCSS.HSA.REI.D.12

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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 and indicates where the inequality changes from true to false.

Tags

CCSS.HSA.REI.D.12