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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![**Topic: Solving a System of Linear Equations Using Elimination**
---
**Instructions:**
Solve the following system of equations:
\[8x + y = 21\]
\[-11x - y = -27\]
**Steps:**
1. **Add the equations to eliminate \( y \):**
Given the equations:
\[ 8x + y = 21 \]
\[-11x - y = -27 \]
Adding them together:
\[ (8x + y) + (-11x - y) = 21 + (-27) \]
\[ 8x - 11x + y - y = -6 \]
\[ -3x = -6 \]
2. **Solve for \( x \):**
Dividing both sides by -3:
\[ x = 2 \]
3. **Substitute \( x \) back into one of the original equations to find \( y \):**
Using the first equation:
\[ 8(2) + y = 21 \]
\[ 16 + y = 21 \]
\[ y = 5 \]
4. **Solution:**
The solution to the system is:
\[ x = 2 \]
\[ y = 5 \]
**Interactive Features:**
- **Input Fields:** Two input fields to enter the values of \( x \) and \( y \).
- **Buttons:**
- A checkmark (✔) to verify the answer.
- A reset button (⟲) to restart the problem.
- A help button (?) to get hints or further explanation.
**Bottom Section:**
- **Explanation Button:** Provides a step-by-step solution to the problem.
- **Check Button:** Validates the input values for \( x \) and \( y \).
---
Feel free to use the provided interface to solve the system and check your understanding of solving linear equations using the elimination method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9a4d797-fb4e-4740-aaae-e63d5fa53795%2F891bd96f-c620-49d0-b08b-f239f75500a6%2Fqdej45_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Solving a System of Linear Equations Using Elimination**
---
**Instructions:**
Solve the following system of equations:
\[8x + y = 21\]
\[-11x - y = -27\]
**Steps:**
1. **Add the equations to eliminate \( y \):**
Given the equations:
\[ 8x + y = 21 \]
\[-11x - y = -27 \]
Adding them together:
\[ (8x + y) + (-11x - y) = 21 + (-27) \]
\[ 8x - 11x + y - y = -6 \]
\[ -3x = -6 \]
2. **Solve for \( x \):**
Dividing both sides by -3:
\[ x = 2 \]
3. **Substitute \( x \) back into one of the original equations to find \( y \):**
Using the first equation:
\[ 8(2) + y = 21 \]
\[ 16 + y = 21 \]
\[ y = 5 \]
4. **Solution:**
The solution to the system is:
\[ x = 2 \]
\[ y = 5 \]
**Interactive Features:**
- **Input Fields:** Two input fields to enter the values of \( x \) and \( y \).
- **Buttons:**
- A checkmark (✔) to verify the answer.
- A reset button (⟲) to restart the problem.
- A help button (?) to get hints or further explanation.
**Bottom Section:**
- **Explanation Button:** Provides a step-by-step solution to the problem.
- **Check Button:** Validates the input values for \( x \) and \( y \).
---
Feel free to use the provided interface to solve the system and check your understanding of solving linear equations using the elimination method.
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