System 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 with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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How do you graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution is where the shaded regions overlap.

Tags

CCSS.HSA.REI.D.12

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What does the solution (3, 3) represent in a system of inequalities?

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The solution (3, 3) represents a point that satisfies all inequalities in the system, meaning it lies in the overlapping shaded region of the graph.

Tags

CCSS.HSA.REI.D.12

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How do you write an inequality from a graph?

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To write an inequality from a graph, identify the boundary line and determine if the line is solid or dashed. Then, find the direction of the shading to determine the inequality symbol (>, <, ≥, ≤).

Tags

CCSS.HSA.REI.D.12

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What is the significance of the number of solutions in a system of inequalities?

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The number of solutions indicates how many points satisfy all inequalities. An infinite number of solutions means the inequalities overlap completely, while no solution means the inequalities do not overlap at all.

Tags

CCSS.HSA.REI.D.12

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What is the relationship between equations and inequalities?

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Inequalities express a range of values that satisfy a condition, while equations express a specific relationship where two expressions are equal. A solution to an inequality can be a range of values, while a solution to an equation is a specific point.

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How can 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 meaning of the variables in a system of equations representing a real-world problem?

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In a system of equations representing a real-world problem, variables typically represent quantities or amounts that need to be determined, such as the number of items or total cost.

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CCSS.8.EE.C.8C

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How do you interpret the solution of a system of equations in a real-world context?

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The solution of a system of equations in a real-world context provides the values of the variables that satisfy all conditions of the problem, often representing quantities or relationships between different entities.

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CCSS.8.EE.C.8C

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What is the first step in solving a system of equations?

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The first step in solving a system of equations is to write the equations clearly and identify the variables involved.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6