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 region on a graph.

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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 (x, y) is in the solution set, substitute the x and y values into the inequality. If the inequality holds true, the point is included in the solution set.

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

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

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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, which is dashed for strict inequalities and solid for non-strict inequalities.

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

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If a point lies on a dashed line, it is not included in the solution set for strict inequalities (< or >). If the line is solid, the point is included.

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Substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.

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