4) X - Y = 4 ------- --- X - Y = 4 -2X + 6Y = 3 -X -X -2X + 6(4-X) = 3 -2X + 24-6X = 3 -8X + 24 = 3 -24 -24 -8X = -21 X = 21/8 y = 4 - 21/8 Y = 11/8 (21/8, 11/8) Y = 4-X
4) X - Y = 4 ------- --- X - Y = 4 -2X + 6Y = 3 -X -X -2X + 6(4-X) = 3 -2X + 24-6X = 3 -8X + 24 = 3 -24 -24 -8X = -21 X = 21/8 y = 4 - 21/8 Y = 11/8 (21/8, 11/8) Y = 4-X
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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---
**Problem 4: Solving the System of Equations**
Given the system of equations:
1. \( X - Y = 4 \)
2. \(-2X + 6Y = 3\)
Steps to solve:
1. Start with the equation \( X - Y = 4 \).
2. Rearrange to express \( Y \) in terms of \( X \):
\[
X - Y = 4 \\
\Rightarrow -X \, \text{(subtracting X from both sides)} \\
Y = 4 - X
\]
3. Substitute \( Y = 4 - X \) into the second equation:
\[
-2X + 6(4 - X) = 3
\]
4. Expand and simplify the equation:
\[
-2X + 24 - 6X = 3
\]
5. Combine like terms:
\[
-8X + 24 = 3
\]
6. Subtract 24 from both sides:
\[
-8X = -21
\]
7. Solve for \( X \):
\[
X = \frac{21}{8}
\]
8. Substitute back to find \( Y \):
\[
Y = 4 - \frac{21}{8} \\
Y = \frac{11}{8}
\]
**Solution:**
\[
(X, Y) = \left(\frac{21}{8}, \frac{11}{8}\right)
\]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42d6d9f4-c49e-4161-9cc8-5846a4f075ec%2Fefa679e2-a267-41ff-9aab-ae142396abdd%2Fcotwy0os_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Here's the transcription of the text document from the image:
---
**Problem 4: Solving the System of Equations**
Given the system of equations:
1. \( X - Y = 4 \)
2. \(-2X + 6Y = 3\)
Steps to solve:
1. Start with the equation \( X - Y = 4 \).
2. Rearrange to express \( Y \) in terms of \( X \):
\[
X - Y = 4 \\
\Rightarrow -X \, \text{(subtracting X from both sides)} \\
Y = 4 - X
\]
3. Substitute \( Y = 4 - X \) into the second equation:
\[
-2X + 6(4 - X) = 3
\]
4. Expand and simplify the equation:
\[
-2X + 24 - 6X = 3
\]
5. Combine like terms:
\[
-8X + 24 = 3
\]
6. Subtract 24 from both sides:
\[
-8X = -21
\]
7. Solve for \( X \):
\[
X = \frac{21}{8}
\]
8. Substitute back to find \( Y \):
\[
Y = 4 - \frac{21}{8} \\
Y = \frac{11}{8}
\]
**Solution:**
\[
(X, Y) = \left(\frac{21}{8}, \frac{11}{8}\right)
\]
---
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