Find all solutions of 62x-34y=16. with y20.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![**Problem Statement:**
Find all solutions of the equation \( 6.2x - 3.4y = 16 \) with \( x \geq 0 \), \( y \geq 0 \).
**Explanation:**
This is a linear equation in two variables, \( x \) and \( y \). The task is to find all pairs \((x, y)\) that satisfy this equation while keeping both variables non-negative.
**Solution Approach:**
1. **Identify the Equation:**
Start with the given equation:
\[
6.2x - 3.4y = 16
\]
2. **Rewrite for \( y \):**
Express \( y \) in terms of \( x \):
\[
3.4y = 6.2x - 16
\]
\[
y = \frac{6.2}{3.4}x - \frac{16}{3.4}
\]
3. **Find Intercepts:**
- **X-Intercept:** Set \( y = 0 \), solve for \( x \).
- **Y-Intercept:** Set \( x = 0 \), solve for \( y \).
4. **Graph Representation:**
Though not shown here, graph the line by plotting the intercepts and identifying the region where both \( x \) and \( y \) are non-negative.
5. **Check for Integer Solutions:**
If necessary, find integer pairs by testing values of \( x \) that result in \( y \) being a non-negative integer, or vice versa.
This approach ensures that you identify all set conditions of \((x,y)\) such that both are non-negative and satisfy the equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa824ef54-0ee2-4591-9058-ff8a94975446%2F37f72929-e8b7-4a71-83c7-034c2affe20e%2Fzoga41p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find all solutions of the equation \( 6.2x - 3.4y = 16 \) with \( x \geq 0 \), \( y \geq 0 \).
**Explanation:**
This is a linear equation in two variables, \( x \) and \( y \). The task is to find all pairs \((x, y)\) that satisfy this equation while keeping both variables non-negative.
**Solution Approach:**
1. **Identify the Equation:**
Start with the given equation:
\[
6.2x - 3.4y = 16
\]
2. **Rewrite for \( y \):**
Express \( y \) in terms of \( x \):
\[
3.4y = 6.2x - 16
\]
\[
y = \frac{6.2}{3.4}x - \frac{16}{3.4}
\]
3. **Find Intercepts:**
- **X-Intercept:** Set \( y = 0 \), solve for \( x \).
- **Y-Intercept:** Set \( x = 0 \), solve for \( y \).
4. **Graph Representation:**
Though not shown here, graph the line by plotting the intercepts and identifying the region where both \( x \) and \( y \) are non-negative.
5. **Check for Integer Solutions:**
If necessary, find integer pairs by testing values of \( x \) that result in \( y \) being a non-negative integer, or vice versa.
This approach ensures that you identify all set conditions of \((x,y)\) such that both are non-negative and satisfy the equation.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
