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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### 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.
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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