Solving 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.

Tags

CCSS.8.EE.C.8B

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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 it mean for a point to be a solution to a system of inequalities?

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A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Tags

CCSS.HSA.REI.D.12

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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 the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).

Tags

CCSS.HSA.REI.D.12

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What is an infinite number of solutions in the context of inequalities?

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An infinite number of solutions occurs when the shaded region of the graph extends indefinitely, meaning there are countless points that satisfy the inequalities.

Tags

CCSS.HSA.REI.D.12

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

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What does it mean if a system of inequalities has no solution?

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A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

Tags

CCSS.HSA.REI.D.12

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

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The boundary line helps to define the regions of solutions. It separates the area where the inequalities are satisfied from the area where they are not.

Tags

CCSS.HSA.REI.D.12

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What is a feasible region in the context of systems of inequalities?

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The feasible region is the area on the graph where all the inequalities in the system are satisfied, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

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How do you identify the vertices of the feasible region?

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The vertices of the feasible region can be found at the points where the boundary lines intersect, which can be determined by solving the equations of the lines.

Tags

CCSS.HSA.REI.D.12