Questions and Answers
What does it mean if a system is consistent?
What does it mean if a system is inconsistent?
What does it mean if a system is independent?
What does it mean if a system is dependent?
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What is it called when the slopes of two equations are the same and the y-intercepts are different?
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What is it called when the slopes of two equations are the same and the y-intercepts are also the same?
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What is it called when the slopes of two equations are different and the y-intercepts are either the same or different?
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Study Notes
Key Terms in Linear Equations
- Consistent: A system of equations with at least one solution.
- Inconsistent: A system of equations that has no solutions.
- Independent: A system of equations with exactly one unique solution.
- Dependent: A system of equations that has infinitely many solutions.
Relationships Based on Slopes and Intercepts
- When two equations have the same slope but different y-intercepts, the system is classified as inconsistent.
- When two equations have the same slope and the same y-intercept, the system is classified as consistent-dependent.
- When two equations have different slopes, the system is classified as consistent-independent, regardless of the y-intercepts.
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Description
Test your understanding of linear equations with this set of flashcards. Each card defines key terms such as 'consistent', 'inconsistent', 'independent', and 'dependent' systems based on their solutions. Perfect for reinforcing concepts from the lesson.
