Questions and Answers
Which ordered pair is in the solution set of the system of linear inequalities: $y > \frac{3}{2} x - 1$ and $y < \frac{3}{2} x - 1$?
Which ordered pair makes both inequalities true: $y > -3x + 3$ and $y > 2x - 2$?
Which system of linear inequalities is represented by the graph?
Which graph shows the solution to the system of linear inequalities: $x - 4y < 4$ and $y < x + 1$?
Signup and view all the answers
Which graph shows the solution to the system of linear inequalities: $y < 2x - 5$ and $y > -3x + 1$?
Signup and view all the answers
Which system of linear inequalities is represented by the graph?
Signup and view all the answers
Which system of linear inequalities is represented by the graph?
Signup and view all the answers
Which ordered pairs are in the solution set of the system of linear inequalities: $y > -\frac{1}{2} x$ and $y < \frac{1}{2} x + 1$?
Signup and view all the answers
Which system of linear inequalities is represented by the graph?
Signup and view all the answers
Which number completes the system of linear inequalities represented by the graph: $y > 2x - 2$ and $x + 4y > ?$?
Signup and view all the answers
Study Notes
Solving Systems of Linear Inequalities
- Evaluating ordered pairs helps determine if they belong to the solution set of a system of linear inequalities.
- For the inequalities ( y > \frac{3}{2} x - 1 ) and ( y < \frac{3}{2} x - 1 ), there is no solution.
- The ordered pair (2,2) satisfies the system ( y > -3x + 3 ) and ( y > 2x - 2 ).
Graph Interpretation
- A graph can visually represent systems of linear inequalities.
- The inequalities represented by the graph are ( y > x - 2 ) and ( y < x + 1 ).
- For the system defined by ( x - 4y < 4 ) and ( y < x + 1 ), the solution is depicted in a specific graph.
- The graph indicating ( y < 2x - 5 ) and ( y > -3x + 1 ) shows another solution set.
Additional Systems and Graphs
- The graph may represent the inequalities ( x + 5y > 5 ) and ( y < 2x + 4 ).
- For the inequalities ( y > x - 2 ) and ( x + 2y < 4 ), there is a corresponding graphical representation.
- A given system of inequalities where ( y > -\frac{1}{2} x ) and ( y < \frac{1}{2} x + 1 ) includes the ordered pairs (5, -2), (3, 1), and (4, 2).
Completing Systems
- The system characterized by ( y > \frac{1}{3} x + 3 ) and ( 3x - y > 2 ) can be interpreted from a graph.
- When completing the system involving ( y > 2x - 2 ), the equation can be completed with ( x + 4y > -12 ).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on solving systems of linear inequalities with these flashcards! Determine which ordered pairs satisfy the given inequalities and analyze their graphical representation. Master the topic to enhance your understanding of linear relationships.
