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What is a two-variable inequality?

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How do you graph a two-variable inequality?

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To graph a two-variable inequality, first graph the corresponding equation as a line. Then, use a dashed line for < or > (not including the line) and a solid line for \leq or \geq (including the line). Finally, shade the appropriate region that satisfies the inequality.

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This inequality represents a situation where the total revenue from selling x glasses of lemonade at $2 each and y bars of lemon squares at $5 each must be at least $150.

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What is the solution set of a system of inequalities?

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The solution set of a system of inequalities is the region on a graph where all the inequalities overlap, representing all the possible solutions that satisfy each inequality.

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The point (4, -2) is a solution to the system of inequalities, meaning it satisfies both inequalities.

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

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The boundary line represents the values where the inequality changes from true to false. Points on the line may or may not be included in the solution set, depending on whether the inequality is strict (< or >) or inclusive (\leq or \geq).

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How do you determine if a point is a solution to a system of inequalities?

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To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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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 (for \leq or \geq), while a dashed line indicates that points on the line are not included (for < or >).

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What is the meaning of the term 'feasible region' in the context of inequalities?

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The feasible region is the area on a graph that satisfies all constraints given by the inequalities in a system, representing all possible solutions.