Podcast
Questions and Answers
Which ordered pairs make both inequalities true? (Check all that apply)
Which ordered pairs make both inequalities true? (Check all that apply)
- (1, 1) (correct)
- (2, 2) (correct)
Graphically, a point is a solution to a system of two inequalities if and only if the point ____.
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 linear inequality will not have a shared solution set with the graphed linear inequality?
- y ≥ x - 1
- y < 3x + 1
- y ≤ 2x + 3
- y > 5/3x + 2 (correct)
Which is the graph of the system x + 3y > -3 and y < 1/2x + 1?
Which is the graph of the system x + 3y > -3 and y < 1/2x + 1?
Which system of inequalities with a solution point is represented by the graph?
Which system of inequalities with a solution point is represented by the graph?
What happens to the system if the inequality sign on both inequalities is reversed?
What happens to the system if the inequality sign on both inequalities is reversed?
What could Miguel write for adding a second inequality to include the solution (1, 1)?
What could Miguel write for adding a second inequality to include the solution (1, 1)?
Determine the relationship between the point (1, -5) and the given system of inequalities.
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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