System 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 if a system of inequalities has no solution?

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A system of inequalities has no solution if there are no points that satisfy all inequalities simultaneously, often represented by parallel lines that never intersect.

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 of inequalities has infinite solutions if there are an unlimited number of points that satisfy all inequalities, typically when the inequalities represent the same line or overlapping regions.

Tags

CCSS.HSA.REI.D.12

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How do you graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the appropriate region for each inequality.

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 in a system of inequalities separates the solution region from the non-solution region. Points on the line are included if the inequality is ≤ or ≥.

Tags

CCSS.HSA.REI.D.12

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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 is the difference between 'y < mx + b' and 'y ≤ mx + b'?

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'y < mx + b' represents a dashed line and does not include points on the line, while 'y ≤ mx + b' represents a solid line and includes points on the line.

Tags

CCSS.HSA.REI.D.12

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What does the term 'feasible region' refer to 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, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

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

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You can identify a system of inequalities from a graph by observing the shaded regions and the boundary lines, then writing the corresponding inequalities that describe those regions.

Tags

CCSS.HSA.REI.D.12

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What is the role of the slope in graphing inequalities?

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The slope indicates the steepness of the line in an inequality. It helps determine the direction of the shading (above or below the line) based on the inequality sign.

Tags

CCSS.HSA.REI.D.12