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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Question
How do I solve with elimination method and determine if these are independent/dependent and consistent/inconsistent?
![## Solving Systems of Equations Using the Elimination Method
To solve a system of linear equations using the elimination method, follow these steps:
### System of Equations:
1. **First Equation:**
\[
3x = 38 - 4y
\]
2. **Second Equation:**
\[
9x = 122 - 13y
\]
### Rearranging:
We rearrange the equations for clarity:
- **Equation 1:**
\[
-38 = -3x - 4y
\]
- **Equation 2:**
\[
-122 = -9x - 13y
\]
### Solution Steps:
1. **Subtraction/Substitution:**
- Subtract the first rearranged equation from the second:
\[
(114 = 9x - 12y)
\]
2. **Simplifying:**
- Simplify further by eliminating \( x \) and combining like terms:
\[
-122 = -9x - 13y
\]
\[
-8 = 0 - 25y
\]
3. **Solve for \( y \):**
- Divide both sides by -25:
\[
y = \frac{8}{25}
\]
### Conclusion:
The solution for \( y \) in the system of equations is \( y = \frac{8}{25} \). Continue to find the value of \( x \) by substituting \( y \) back into either equation if needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f2568c7-b3c1-4dcf-b04a-329e36104d6c%2F07a359bc-20b1-43a5-801f-a98bcf318409%2Ffi3vrb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Solving Systems of Equations Using the Elimination Method
To solve a system of linear equations using the elimination method, follow these steps:
### System of Equations:
1. **First Equation:**
\[
3x = 38 - 4y
\]
2. **Second Equation:**
\[
9x = 122 - 13y
\]
### Rearranging:
We rearrange the equations for clarity:
- **Equation 1:**
\[
-38 = -3x - 4y
\]
- **Equation 2:**
\[
-122 = -9x - 13y
\]
### Solution Steps:
1. **Subtraction/Substitution:**
- Subtract the first rearranged equation from the second:
\[
(114 = 9x - 12y)
\]
2. **Simplifying:**
- Simplify further by eliminating \( x \) and combining like terms:
\[
-122 = -9x - 13y
\]
\[
-8 = 0 - 25y
\]
3. **Solve for \( y \):**
- Divide both sides by -25:
\[
y = \frac{8}{25}
\]
### Conclusion:
The solution for \( y \) in the system of equations is \( y = \frac{8}{25} \). Continue to find the value of \( x \) by substituting \( y \) back into either equation if needed.
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