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What is a system of linear inequalities?

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A system of linear inequalities is a set of two or more inequalities that involve the same variables. The solution is the region where the graphs of the inequalities overlap.

Tags

CCSS.HSA.REI.D.12

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for 'greater than' or 'less than' and a solid line for 'greater than or equal to' or 'less than or equal to'. Then shade the appropriate region based on the inequality.

Tags

CCSS.HSA.REI.D.12

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What does the solution region of a system of linear inequalities represent?

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The solution region represents all the possible solutions that satisfy all inequalities in the system.

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 it mean if a system of linear inequalities has no solution?

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A system has no solution if the graphs of the inequalities do not intersect, meaning there is no region that satisfies all inequalities.

Tags

CCSS.HSA.REI.D.12

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What does it mean if a system of linear inequalities has infinitely many solutions?

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A system has infinitely many solutions if the inequalities overlap in such a way that there are countless points that satisfy all inequalities, often when the lines are the same or parallel.

Tags

CCSS.HSA.REI.D.12

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How can 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 significance of the boundary line in a linear inequality?

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The boundary line separates the solution region from the non-solution region and helps to identify which side of the line satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

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What does the notation 'y > mx + b' represent?

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This notation represents a linear inequality where 'm' is the slope and 'b' is the y-intercept, indicating that the region above the line is the solution.

Tags

CCSS.HSA.REI.D.12

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What is the role of the slope in a linear inequality?

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The slope determines the steepness of the line and the direction in which the inequality opens (upward or downward).