
Solving Systems of Inequalities
Flashcard
•
Mathematics
•
9th Grade
•
Practice Problem
•
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 with the same variables. The solution is the set of all points that satisfy all inequalities in the system.
2.
FLASHCARD QUESTION
Front
How do you graph a linear inequality?
Back
To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the region that satisfies the inequality.
3.
FLASHCARD QUESTION
Front
What does it mean if a point is a solution to a system of inequalities?
Back
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.
4.
FLASHCARD QUESTION
Front
What is the difference between '≤' and '<'?
Back
'≤' means 'less than or equal to', indicating that the boundary line is included in the solution. '<' means 'less than', indicating that the boundary line is not included.
5.
FLASHCARD QUESTION
Front
What is the significance of the boundary line in a graph of inequalities?
Back
The boundary line represents the points where the inequality changes from true to false. It divides the coordinate plane into regions that satisfy or do not satisfy the inequality.
6.
FLASHCARD QUESTION
Front
How can you determine if a point is a solution to a linear inequality?
Back
To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.
7.
FLASHCARD QUESTION
Front
What does it mean if a system of inequalities has no solution?
Back
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.
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