Questions and Answers
Identify the vertex of the system of inequalities: (____, ____)
( , )
Identify the system of inequalities as bounded or unbounded.
Which point satisfies the inequality $2x + 3y ≤ -5$?
Which inequalities produce a solid boundary line?
Signup and view all the answers
What is the region of overlap called for a system of linear inequalities?
Signup and view all the answers
You need to shade the correct region on a graph for this equation: -x + y ≤ -1. What do you need to do?
Signup and view all the answers
Graph the system of inequalities: -x + y > -2, x + 2y < 2.
Signup and view all the answers
Study Notes
System of Inequalities
- Vertex of the system of inequalities is denoted as (____, ____).
- Identify if the system is bounded (enclosed) or unbounded (extending infinitely).
Solution Region & Points
- To determine which points lie within the solution region, analyze the following coordinates:
- (-5, 4)
- (2, 5)
- (-5, -2)
Satisfying Inequalities
- The point that satisfies the inequality 2x + 3y ≤ -5 is (-4, 0).
- Other given points include:
- (0, -1)
- (4, 0)
Solid Boundary Lines
- An inequality that produces a solid boundary line is ½x + y ≤ 12.
- Inequalities leading to dashed lines include:
- -3x - y < 1
- x + 5y ≠ 2
- -8x - 7y > 5
Overlapping Regions
- The region of overlap where all shaded areas of the inequalities intersect is called the intersection.
Graphing Inequalities
- Shading is required to reflect the solution to the inequality -x + y ≤ -1 on a graph.
- A graph must be created for the system of inequalities:
- -x + y > -2
- x + 2y < 2
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on systems of inequalities with this set of flashcards from Abeka Algebra II Quiz 17. Each card challenges you to identify critical points, analyze boundedness, and find solutions within specified regions. Perfect for reinforcing your understanding of graphing and inequalities.
