Linear Inequalities with Systems

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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 (such as <, >, ≤, or ≥).

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What does the graph of a linear inequality represent?

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The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of the boundary line.

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

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How do you determine if a point is a solution to a linear inequality?

Back

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

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Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the coordinate plane into two regions, one that contains solutions to the inequalities and one that does not.

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What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality represented by a solid line, it is included as a solution; if represented by a dashed line, it is not included.

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How can you identify the solution set of a system of inequalities?

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The solution set of a system of inequalities is the region where the shaded areas of all inequalities overlap.

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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 that are solved simultaneously.

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What does the term 'solution' refer to in the context of inequalities?

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A solution refers to any ordered pair (x, y) that satisfies the inequality.