Linear Inequalities and 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 compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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What does the solution set of a linear inequality represent?

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The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

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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, shade the region that represents the solution set based on the inequality symbol.

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

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What does it mean for a point to be a solution to a linear inequality?

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A point is a solution to a linear inequality if it satisfies the inequality when the coordinates are substituted into the inequality.

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How can you determine if a point is part of the solution set?

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To determine if a point is part of the solution set, substitute the point's coordinates into the inequality and check if the statement is true.

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What is a system of linear inequalities?

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A system of linear inequalities consists of two or more linear inequalities that are considered together.

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How do you find the solution set of a system of linear inequalities?

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To find the solution set of a system of linear inequalities, graph each inequality and identify the region where the shaded areas overlap.

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

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The boundary line helps to define the limits of the solution set and indicates whether points on the line are included or excluded.

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Can a point be a solution to one inequality but not another in a system?

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Yes, a point can satisfy one inequality in a system while not satisfying another, meaning it may be part of the solution set for one inequality but not for the system as a whole.