system of inequalities introduction

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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 that share the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.

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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 does it mean for a point to be part of the solution set?

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A point is part of the solution set if it satisfies all inequalities in the system, meaning it lies in the region defined by the inequalities.

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What is the graphical representation of a system of inequalities?

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The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of the inequalities.

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

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The boundary line represents the points where the inequality changes from true to false. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

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What does it mean if a point lies above a boundary line in a system of inequalities?

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If a point lies above a boundary line, it means that the point satisfies the inequality associated with that line.

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What does it mean if a point lies below a boundary line in a system of inequalities?

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If a point lies below a boundary line, it means that the point does not satisfy the inequality associated with that line.

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How can you identify a solution from a list of points?

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To identify a solution from a list of points, substitute each point into the inequalities. The points that satisfy all inequalities are the solutions.

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What is an ordered pair in the context of a system of inequalities?

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An ordered pair is a pair of numbers (x, y) that represents a point on the coordinate plane.

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What is the difference between a solution and a non-solution in a system of inequalities?

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A solution satisfies all inequalities in the system, while a non-solution does not satisfy at least one inequality.