Systems of Inequalities

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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 points that satisfy all inequalities in the system.

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What does it mean for two lines to be parallel?

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Two lines are parallel if they have the same slope and will never intersect.

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What does it mean for two lines to be perpendicular?

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Two lines are perpendicular if the product of their slopes is -1. This means that one line's slope is the negative reciprocal of the other's.

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How do you write an equation in point-slope form?

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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 point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the standard form of a linear equation?

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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 each inequality.