Solutions to Systems of Inequalities - Activity

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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.

Tags

CCSS.HSA.REI.D.12

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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 a solution to a system of inequalities?

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A point is a solution if it lies in the region defined by the inequalities, meaning it satisfies all the conditions set by the inequalities.

Tags

CCSS.HSA.REI.D.12

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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.

Tags

CCSS.HSA.REI.D.12

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

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Boundary lines represent the limits of the inequalities. If the inequality is strict (e.g., < or >), the line is dashed; if it includes equality (e.g., ≤ or ≥), the line is solid.

Tags

CCSS.HSA.REI.D.12

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How can you identify a solution from a list of ordered pairs?

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Substitute each ordered pair into the inequalities. The pairs that satisfy all inequalities are the solutions.

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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, while a non-solution does not meet at least one of the inequalities.

Tags

CCSS.HSA.REI.D.12

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What does it mean if a point is on the boundary line of an inequality?

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If a point is on the boundary line, it may or may not be a solution, depending on whether the inequality includes equality (≤ or ≥) or not (< or >).

Tags

CCSS.HSA.REI.D.12

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How do you graph a system of inequalities?

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1. Graph each inequality as a line. 2. Use a dashed line for strict inequalities and a solid line for inclusive inequalities. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

Tags

CCSS.HSA.REI.D.12

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What is an ordered pair?

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An ordered pair is a pair of numbers (x, y) that represent a point on a coordinate plane, where x is the horizontal coordinate and y is the vertical coordinate.

Tags

CCSS.5.G.A.1