Systems of Linear Inequalities Flashcard

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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 share the same variables. The solution set is the region where the graphs of the inequalities overlap.

Tags

CCSS.HSA.REI.D.12

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How do you determine if a point is in the solution set of a linear inequality?

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

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What does it mean for a point to satisfy a linear inequality?

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A point satisfies a linear inequality if, when its coordinates are substituted into the inequality, the resulting statement is true.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a half-plane divided by a boundary line. The line is solid if the inequality is inclusive (≤ or ≥) and dashed if it is exclusive (< or >).

Tags

CCSS.HSA.REI.D.12

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What is the difference between a solid line and a dashed line in the graph of linear 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 do you graph a system of linear inequalities?

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To graph a system of linear inequalities, graph each inequality on the same coordinate plane, shading the appropriate half-plane for each. The solution set is where the shaded regions overlap.

Tags

CCSS.HSA.REI.D.12

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What is the solution set of a system of linear inequalities?

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The solution set of a system of linear inequalities is the set of all points (x, y) that satisfy all inequalities in the system, represented graphically as the overlapping shaded region.

Tags

CCSS.HSA.REI.D.12

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What is the significance of the boundary line in a linear inequality?

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The boundary line in a linear inequality separates the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Tags

CCSS.HSA.REI.D.12

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How can you check if a point is in the solution set of a system of inequalities?

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To check if a point is in the solution set of a system of inequalities, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is in the solution set.

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