Systems of Linear Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥) instead of an equal sign.

Tags

CCSS.7.EE.B.4B

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

Tags

CCSS.HSA.REI.D.12

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

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The solution set of a system of linear inequalities represents all the points (x, y) that satisfy all inequalities in the system simultaneously.

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 set (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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How can you determine if a point is a solution to a linear inequality?

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To determine if a point is a solution to a linear inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is part of the solution set.

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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 linear inequalities that are considered together. The solution is the intersection of the solution sets of each inequality.

Tags

CCSS.HSA.REI.D.12

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What does it mean for a point to be 'not part of the solution set'?

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A point is 'not part of the solution set' if it does not satisfy at least one of the inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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How do you write a linear equation from a word problem involving costs?

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To write a linear equation from a word problem involving costs, identify the variables representing the quantities, set up an equation based on the relationships described in the problem, and include the total cost as a constant.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is the significance of the coefficients in a linear equation?

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The coefficients in a linear equation represent the rate of change or the slope of the line, indicating how much the dependent variable changes for a unit change in the independent variable.

Tags

CCSS.HSF.LE.B.5

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What is the graphical representation of a system of linear inequalities?

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The graphical representation of a system of linear inequalities is the shaded region where all the inequalities overlap, showing all possible solutions.

Tags

CCSS.HSA.REI.D.12