Graphing systems of Inequalities

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•
Mathematics
•
9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a system of inequalities?
Back
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.
2.
FLASHCARD QUESTION
Front
What does it mean if two inequalities are parallel in a system?
Back
If two inequalities are parallel, it means they have the same slope but different y-intercepts. The solution may be empty, or it may include overlapping shaded regions.
3.
FLASHCARD QUESTION
Front
How do you graph an inequality with a 'greater than' symbol?
Back
To graph an inequality with a 'greater than' symbol, use a dashed line to indicate that points on the line are not included in the solution set, and shade the region above the line.
4.
FLASHCARD QUESTION
Front
What is the difference between a solid line and a dashed line in graphing inequalities?
Back
A solid line indicates that points on the line are included in the solution set (for 'greater than or equal to' or 'less than or equal to'), while a dashed line indicates that points on the line are not included (for 'greater than' or 'less than').
5.
FLASHCARD QUESTION
Front
How do you determine if a point is a solution to a system of inequalities?
Back
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.
6.
FLASHCARD QUESTION
Front
What does the shaded region in a graph of inequalities represent?
Back
The shaded region represents all the possible solutions to the system of inequalities. Points within this region satisfy all inequalities.
7.
FLASHCARD QUESTION
Front
What is the significance of the intersection of shaded regions in a system of inequalities?
Back
The intersection of shaded regions represents the set of solutions that satisfy all inequalities in the system.
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