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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![### Solving a System of Linear Equations Using Substitution
**Topic**: Linear Systems
In this section, we will learn how to solve a system of linear equations using the substitution method.
**Problem:**
Solve the system of linear equations using substitution:
\[
-5x + 3y = 14
\]
\[
y = 2x + 5
\]
**Step-by-Step Solution:**
1. Start with the second equation:
\[ y = 2x + 5 \]
2. Substitute \( y \) in the first equation with the expression from the second equation:
\[ -5x + 3(2x + 5) = 14 \]
3. Simplify the equation:
\[
-5x + 6x + 15 = 14
\]
\[
x + 15 = 14
\]
\[
x = -1
\]
4. Substitute \( x \) back into the second equation to find \( y \):
\[ y = 2(-1) + 5 \]
\[ y = -2 + 5 \]
\[ y = 3 \]
**Solution:**
\[
x = -1, \quad y = 3
\]
Make sure to input your values of \( x \) and \( y \) in the respective fields on the educational website and click "Check" to verify your answer. If you need further explanation, you can always click on the "Explanation" button for a detailed walkthrough of the steps involved.
**Visual Aids:**
- There is a box for entering the values of \( x \) and \( y \).
- There are buttons next to the boxes including 'x', a refresh icon for resetting the values, and a question mark for help or more information.
Make use of these interactive tools to enhance your understanding and practice of solving linear equations using substitution.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce668d18-9889-43e2-93d7-4b1cfcddd4ed%2F15ec43a4-4869-4592-af8c-3d1f7c8f70ed%2F7gij8ea_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving a System of Linear Equations Using Substitution
**Topic**: Linear Systems
In this section, we will learn how to solve a system of linear equations using the substitution method.
**Problem:**
Solve the system of linear equations using substitution:
\[
-5x + 3y = 14
\]
\[
y = 2x + 5
\]
**Step-by-Step Solution:**
1. Start with the second equation:
\[ y = 2x + 5 \]
2. Substitute \( y \) in the first equation with the expression from the second equation:
\[ -5x + 3(2x + 5) = 14 \]
3. Simplify the equation:
\[
-5x + 6x + 15 = 14
\]
\[
x + 15 = 14
\]
\[
x = -1
\]
4. Substitute \( x \) back into the second equation to find \( y \):
\[ y = 2(-1) + 5 \]
\[ y = -2 + 5 \]
\[ y = 3 \]
**Solution:**
\[
x = -1, \quad y = 3
\]
Make sure to input your values of \( x \) and \( y \) in the respective fields on the educational website and click "Check" to verify your answer. If you need further explanation, you can always click on the "Explanation" button for a detailed walkthrough of the steps involved.
**Visual Aids:**
- There is a box for entering the values of \( x \) and \( y \).
- There are buttons next to the boxes including 'x', a refresh icon for resetting the values, and a question mark for help or more information.
Make use of these interactive tools to enhance your understanding and practice of solving linear equations using substitution.
---
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