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Questions and Answers
What is it called when a linear system has exactly one solution?
What is it called when a linear system has exactly one solution?
- Exactly One Solution (correct)
- Infinitely Many Solutions
- No Solution
- Dependent System
What does it mean if a linear system has infinitely many solutions?
What does it mean if a linear system has infinitely many solutions?
consistent and dependent, lines with the same slope and same y-intercept.
What characterizes a linear system with no solution?
What characterizes a linear system with no solution?
inconsistent, same slope with different y-intercepts.
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Study Notes
Linear Systems Classifications
-
Exactly One Solution:
- Characterized by consistent and independent systems.
- Represented by intersecting lines that have different slopes, ensuring a unique point of intersection.
-
Infinitely Many Solutions:
- Defined as consistent and dependent systems.
- Occurs when the lines have the same slope and the same y-intercept, making them identical.
-
No Solution:
- Classified as inconsistent systems.
- Features parallel lines that have the same slope but different y-intercepts, leading to no points of intersection.
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