System of Inequalities

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
+1
Standards-aligned
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15 questions
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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 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
2.
FLASHCARD QUESTION
Front
How do you graph a system of inequalities?
Back
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
3.
FLASHCARD QUESTION
Front
What does the solution (3, 3) represent in a system of inequalities?
Back
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
4.
FLASHCARD QUESTION
Front
How do you write an inequality from a graph?
Back
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
5.
FLASHCARD QUESTION
Front
What is the significance of the number of solutions in a system of inequalities?
Back
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
6.
FLASHCARD QUESTION
Front
What is the relationship between equations and inequalities?
Back
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.
7.
FLASHCARD QUESTION
Front
How can 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.
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