Linear inequalities (two variables)

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What is a linear inequality in two variables?

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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 ordered pairs (x, y) that satisfy the inequality, often visualized as a shaded region on a graph.

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

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

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What is the significance of the shaded area in the graph of a linear inequality?

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The shaded area in the graph of a linear inequality indicates all the possible solutions to the inequality. Points within this area satisfy the inequality.

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

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What is the difference between a strict and non-strict inequality?

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A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (\leq or \geq) includes the boundary line in the solution set.

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How can 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 appropriate region based on the inequality sign.

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What does it mean if a point is not in the shaded area of a linear inequality?

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If a point is not in the shaded area of a linear inequality, it means that the point does not satisfy the inequality.