Two- Variable Inequalities

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What is a two-variable inequality?

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What does the graph of a two-variable inequality represent?

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The graph of a two-variable inequality represents all the solutions (ordered pairs) that satisfy the inequality, often shown as a shaded region on a coordinate plane.

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What is the significance of the boundary line in a two-variable inequality?

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The boundary line is the line that represents the equation formed by replacing the inequality sign with an equal sign. It divides the plane into two regions, one of which contains the solutions to the inequality.

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When is the boundary line included in the solution set?

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When is the boundary line not included in the solution set?

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The boundary line is not included in the solution set if the inequality is either < or >.

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How do you determine if a point is a solution to a two-variable inequality?

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

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The solution set includes all points above the parabola defined by the equation, not including the points on the parabola itself.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (\leq, \geq) do include the boundary line.