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Questions and Answers
What does it mean if a system is consistent?
What does it mean if a system is consistent?
- A system has infinitely many solutions.
- A system has at least one solution. (correct)
- A system has no solutions.
- A system has one solution.
What does it mean if a system is inconsistent?
What does it mean if a system is inconsistent?
- A system has at least one solution.
- A system has infinitely many solutions.
- A system has no solutions. (correct)
- A system has one solution.
What does it mean if a system is independent?
What does it mean if a system is independent?
- A system has at least one solution.
- A system has one solution. (correct)
- A system has infinitely many solutions.
- A system has no solutions.
What does it mean if a system is dependent?
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?
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?
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?
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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