Podcast
Questions and Answers
Which ordered pairs are in the solution set of the system of linear inequalities? $y > rac{1}{2} x$ and $y < -3x + 3$ and $y > 2x - 2$
Which ordered pairs are in the solution set of the system of linear inequalities? $y > rac{1}{2} x$ and $y < -3x + 3$ and $y > 2x - 2$
Which ordered pair makes both inequalities true? $y < -x + 1$ and $y > x$
Which ordered pair makes both inequalities true? $y < -x + 1$ and $y > x$
Which number completes the system of linear inequalities represented by the graph? $y < -2x - 1$ and $y > -2x +
Which number completes the system of linear inequalities represented by the graph? $y < -2x - 1$ and $y > -2x +
2
Which ordered pair makes both inequalities true? $y > -2x + 3$ and $y < x - 2$
Which ordered pair makes both inequalities true? $y > -2x + 3$ and $y < x - 2$
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This is true about the solution to the system of inequalities shown: $y < rac{1}{3}x - 1$ and $y > rac{2}{3}x + 3$ and $y < - rac{1}{3}x + 2$.
This is true about the solution to the system of inequalities shown: $y < rac{1}{3}x - 1$ and $y > rac{2}{3}x + 3$ and $y < - rac{1}{3}x + 2$.
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Which system of linear inequalities is represented by the graph? line by 3 and -3
Which system of linear inequalities is represented by the graph? line by 3 and -3
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Which ordered pair makes both inequalities true? $y < 3x - 1$ and $y > -x + 4$
Which ordered pair makes both inequalities true? $y < 3x - 1$ and $y > -x + 4$
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Which system of linear inequalities is represented by the graph? $y < x + 1$ and $y > x - 2$
Which system of linear inequalities is represented by the graph? $y < x + 1$ and $y > x - 2$
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Which ordered pairs make both inequalities true? Check all that apply. $y < 5x + 2$ and $y > x + 1$
Which ordered pairs make both inequalities true? Check all that apply. $y < 5x + 2$ and $y > x + 1$
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Which ordered pair is in the solution set of the system of linear inequalities? $y > x - 1$ and $y < x - 1$
Which ordered pair is in the solution set of the system of linear inequalities? $y > x - 1$ and $y < x - 1$
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Study Notes
Systems of Linear Inequalities
- Ordered pairs must satisfy all inequalities in the system to be part of the solution set.
- Example of a valid ordered pair: (2,2) meets the criteria for the inequalities y > 1/2 x and y < -3x + 3, and y > 2x - 2.
Inequality Evaluation
- Ordered pair (-2, 2) satisfies the inequalities y < -x + 1 and y > x.
- The number 2 is crucial in completing the system represented by y < -2x - 1 and another inequality.
Specific Ordered Pairs
- The pair (3,0) is valid for the inequalities y > -2x + 3 and y < x - 2.
- Another valid pair (4,0) satisfies the conditions y < 3x - 1 and y > -x + 4.
Graphical Representations
- A graph can illustrate the constraints y < 1/3x - 1, y 2/3x + 3, and y < -1/3x + 2.
- Systems represented by a graph can include multiple inequalities, like y > 1/3 x + 3 and 3x - y > 2.
- Example graph systems: x - 5y < -5 and y < -2x - 4, or x + 5y > 5 and y < 2x + 4.
No Solution Scenarios
- An ordered pair falling into no valid solution zone occurs when y > x - 1 and y < x - 1, resulting in no solution.
Summary of Ordered Pairs and Inequalities
- Graphs identify valid pairs and systems, e.g., (3,5) satisfying y < 5x + 2 and y > x + 1.
- Systems often consist of linear inequalities that delineate regions on a graph where solutions can be found.
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Description
Test your knowledge of systems of linear inequalities with this informative quiz. Evaluate ordered pairs and apply graphical representations to identify valid solutions. Explore various scenarios including those with no solutions and become proficient in recognizing valid inequalities.
