
Solving Systems of Linear Inequalities
Flashcard
•
Mathematics
•
8th - 9th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a system of linear inequalities?
Back
A system of linear inequalities is a set of two or more linear inequalities that share the same variables. The solution to the system is the set of all points that satisfy all inequalities in the system.
2.
FLASHCARD QUESTION
Front
How do you graph a linear inequality in two variables?
Back
To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for inequalities that do not include equality (e.g., < or >) and a solid line for those that do (e.g., ≤ or ≥). Then, shade the region that satisfies the inequality.
3.
FLASHCARD QUESTION
Front
What does it mean for a point to be a solution of a system of linear inequalities?
Back
A point is a solution of a system of linear inequalities if it satisfies all inequalities in the system. This means that when the coordinates of the point are substituted into each inequality, the resulting statements are true.
4.
FLASHCARD QUESTION
Front
What is the difference between a solid line and a dashed line when graphing inequalities?
Back
A solid line indicates that the points on the line are included in the solution set (for ≤ or ≥ inequalities), while a dashed line indicates that the points on the line are not included (for < or > inequalities).
5.
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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.
6.
FLASHCARD QUESTION
Front
What is the significance of the shaded region in the graph of a system of inequalities?
Back
The shaded region represents all possible solutions to the system of inequalities. Any point within this region satisfies all inequalities in the system.
7.
FLASHCARD QUESTION
Front
What is the graphical representation of the inequality y > 2x - 3?
Back
The graphical representation is a dashed line for the equation y = 2x - 3, with the region above the line shaded, indicating that y must be greater than the values on the line.
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