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 #6: Solving a System by Substitution**
To solve the system of equations using substitution, follow these steps:
1. **Equations Given:**
\[
x = 2y + 2
\]
\[
2x - 5y = 1
\]
2. **Substitute the Expression:**
Substitute \( x = 2y + 2 \) into the second equation:
\[
2(2y + 2) - 5y = 1
\]
3. **Solve for \( y \):**
\[
4y + 4 - 5y = 1
\]
\[
-y + 4 = 1
\]
\[
-y = 1 - 4
\]
\[
-y = -3
\]
\[
y = 3
\]
4. **Find \( x \):**
Substitute \( y = 3 \) back into the expression for \( x \):
\[
x = 2(3) + 2
\]
\[
x = 6 + 2
\]
\[
x = 8
\]
5. **Solution:**
The solution to the system of equations is \((8, 3)\).
**The Solution is \((8, 3)\)**
Use the substitution method carefully to find the values of \( x \) and \( y \) that satisfy both equations. Check the solution by plugging back into the original equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47233639-9d53-42f0-bc37-bcddb016235d%2F4e6f99ed-0d96-4600-8b0b-c6c6da8ac61d%2Fualpjbm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem #6: Solving a System by Substitution**
To solve the system of equations using substitution, follow these steps:
1. **Equations Given:**
\[
x = 2y + 2
\]
\[
2x - 5y = 1
\]
2. **Substitute the Expression:**
Substitute \( x = 2y + 2 \) into the second equation:
\[
2(2y + 2) - 5y = 1
\]
3. **Solve for \( y \):**
\[
4y + 4 - 5y = 1
\]
\[
-y + 4 = 1
\]
\[
-y = 1 - 4
\]
\[
-y = -3
\]
\[
y = 3
\]
4. **Find \( x \):**
Substitute \( y = 3 \) back into the expression for \( x \):
\[
x = 2(3) + 2
\]
\[
x = 6 + 2
\]
\[
x = 8
\]
5. **Solution:**
The solution to the system of equations is \((8, 3)\).
**The Solution is \((8, 3)\)**
Use the substitution method carefully to find the values of \( x \) and \( y \) that satisfy both equations. Check the solution by plugging back into the original equations.
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