Numbers of Solutions of Systems of Linear Equations different slopes same slope different y-intercepts same slope same y-intercept The lines The lines The lines are so there is so there are so there are solution. solutions. solutions.
Numbers of Solutions of Systems of Linear Equations different slopes same slope different y-intercepts same slope same y-intercept The lines The lines The lines are so there is so there are so there are solution. solutions. solutions.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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
Transcribed Image Text:### Solving Linear Systems - Educational Resource
---
#### Vocabulary and Key Concepts
1. **Use the following vocabulary to fill in the boxes below:**
- *No / Intersect / are parallel / Infinite / one / the same*
---
#### Numbers of Solutions of Systems of Linear Equations
1. **Different Slopes**
- **Diagram:** Shows two lines intersecting at a single point on a graph.
- **Explanation:** The lines intersect, so there is ***one*** solution.
2. **Same Slope, Different Y-Intercepts**
- **Diagram:** Shows two parallel lines on a graph that never intersect.
- **Explanation:** The lines are ***parallel***, so there are ***no*** solutions.
3. **Same Slope, Same Y-Intercept**
- **Diagram:** Shows a single line, implying that two lines are exactly on top of each other.
- **Explanation:** The lines are ***the same***, so there are ***infinite*** solutions.
---
2. **In a sentence explain what is the solution to a system of equations?**
- A solution to a system of equations is the point or set of points that satisfy all equations simultaneously.
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