Podcast
Questions and Answers
What is an independent system?
What is an independent system?
A system that has exactly one solution.
What is a dependent system?
What is a dependent system?
A system that has infinite solutions.
What is an inconsistent system?
What is an inconsistent system?
A system that has no solution.
What is a consistent system?
What is a consistent system?
When solving a system algebraically, how can you determine if the system has infinite solutions?
When solving a system algebraically, how can you determine if the system has infinite solutions?
When solving a system algebraically, how can you determine if the system has no solution?
When solving a system algebraically, how can you determine if the system has no solution?
When solving a system algebraically, if the resulting statement is 0 = 0, how does the graph look and how do you classify the system?
When solving a system algebraically, if the resulting statement is 0 = 0, how does the graph look and how do you classify the system?
When solving a system algebraically, if you're able to solve for x, how does the graph look and how do you classify the system?
When solving a system algebraically, if you're able to solve for x, how does the graph look and how do you classify the system?
When solving a system algebraically, if your resulting equation is -2=2, how does the graph look and how do you classify the system?
When solving a system algebraically, if your resulting equation is -2=2, how does the graph look and how do you classify the system?
Give an example of a dependent system.
Give an example of a dependent system.
Flashcards
Independent System
Independent System
A system of equations with one unique solution.
Dependent System
Dependent System
A system of equations with infinitely many solutions.
Inconsistent System
Inconsistent System
A system of equations with no solutions.
Consistent System
Consistent System
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Identifying Infinite Solutions
Identifying Infinite Solutions
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Identifying No Solutions
Identifying No Solutions
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Coinciding Lines System
Coinciding Lines System
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Intersecting Lines System
Intersecting Lines System
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Parallel Lines System
Parallel Lines System
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Dependent System Example
Dependent System Example
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Study Notes
Classifying Systems of Linear Equations
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Independent System: Contains exactly one solution; represented visually by two lines that intersect at a single point.
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Dependent System: Has infinitely many solutions; shown graphically as coinciding lines, indicating they are the same line.
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Inconsistent System: Results in no solutions; depicted by parallel lines that never intersect.
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Consistent System: At least one solution exists; this term encompasses both independent and dependent systems.
Solving Systems Algebraically
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Infinite Solutions Determination: If the resulting equation is a TRUE STATEMENT (e.g., 7=7), it indicates infinite solutions.
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No Solution Determination: If resolving leads to a FALSE STATEMENT (e.g., 2=5), it signifies that the system has no solutions.
Graphical Representations and Classifications
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Resulting Equation: 0 = 0: Indicates coinciding lines; classified as consistent and dependent due to infinite solutions.
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Solving for x Successfully: Represents lines intersecting at exactly one point, classifying the system as consistent and independent.
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Resulting Equation: -2 = 2: Represents a contradiction; visual representation shows parallel lines, classifying it as inconsistent.
Example of a Dependent System
- Dependent System Example:
- Equation 1: y = 2x + 3
- Equation 2: -3 + y = 2x
- Both equations represent the same line, confirming the nature of dependence.
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