Questions and Answers
Which ordered pairs make both inequalities true? (Check all that apply)
Graphically, a point is a solution to a system of two inequalities if and only if the point ____.
lies in the shaded regions of both the top and bottom inequalities.
Which linear inequality will not have a shared solution set with the graphed linear inequality?
Which is the graph of the system x + 3y > -3 and y < 1/2x + 1?
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Which system of inequalities with a solution point is represented by the graph?
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What happens to the system if the inequality sign on both inequalities is reversed?
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What could Miguel write for adding a second inequality to include the solution (1, 1)?
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Determine the relationship between the point (1, -5) and the given system of inequalities.
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Study Notes
Ordered Pairs and Inequalities
- Points (1, 1) and (2, 2) are valid solutions that satisfy both inequalities in the system.
Graphical Solutions
- A point is considered a solution to a system of two inequalities if it lies within the shaded regions of both inequalities.
Inequality Analysis
- The inequality y > (5/3)x + 2 does not overlap with the graphed linear inequality, indicating no shared solution set.
Graph Identification
- The system defined by the inequalities x + 3y > -3 and y < (1/2)x + 1 corresponds to Graph 4.
Solution Representation in Graphs
- The inequalities y > 2x + 2 and y < (-1/2)x + 1 have the solution point (-3, 1) depicted within the graph.
System Inequalities and Solutions
- Reversing the inequality signs in the system changes its solution status. Originally, there's no overlap; reversed, it presents an infinite number of solutions.
Second Inequality Addition
- To include the point (1, 1) in Han's graph, Mr. Hernandez could add the inequality y ≤ 2x - 1.
Point Relationship with Inequalities
- The point (1, -5) satisfies the first inequality (y ≤ 3x + 2) but fails to satisfy the second (y > -2x - 3). Graphically, it falls within the first shaded area but not in the inclusion of the second inequality, confirming it as a non-solution.
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Test your understanding of systems of linear inequalities with these flashcards. Each card challenges you to determine the solutions and graphical representations of inequalities. Perfect for review or quick learning!
