## Elementary Linear Algebra 7th Edition

Published by Cengage Learning

# Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises - Page 10: 41

#### Answer

Ans: $x=-\frac{1}{3}, y=-\frac{2}{3}$

#### Work Step by Step

Step 1: Simplify second equation $\frac{1}{5}x+\frac{2}{5}y=-\frac{1}{3}$ $3x+6y=-5$ $6y=-5-3x$ Step 2: Put $6y$ to one side on first equation $3y=9x+1$ $6y=18x+2$ Step 3: The other side of $6y$ are equal, so make an equation and solve $x$ $18x+2=-5-3x$ $21x=-7$ $x=-\frac{1}{3}$ Step 4: Substitute $x$ to one of the equations $9\times(-\frac{1}{3})-3y=-1$ $-3y=2$ $y=-\frac{2}{3}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
The text passage contains a mathematical problem involving a system of linear equations and provides a step-by-step solution to find the values of \( x \) and \( y \).
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Elementary Linear Algebra 7th Edition

Published by Cengage Learning

# Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises - Page 10: 41

#### Answer

Ans: $x=-\frac{1}{3}, y=-\frac{2}{3}$

#### Work Step by Step

Step 1: Simplify second equation $\frac{1}{5}x+\frac{2}{5}y=-\frac{1}{3}$ $3x+6y=-5$ $6y=-5-3x$ Step 2: Put $6y$ to one side on first equation $3y=9x+1$ $6y=18x+2$ Step 3: The other side of $6y$ are equal, so make an equation and solve $x$ $18x+2=-5-3x$ $21x=-7$ $x=-\frac{1}{3}$ Step 4: Substitute $x$ to one of the equations $9\times(-\frac{1}{3})-3y=-1$ $-3y=2$ $y=-\frac{2}{3}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
user
The text passage contains a mathematical problem involving a system of linear equations and provides a step-by-step solution to find the values of \( x \) and \( y \).

TYPE: SINGLE_QUESTION_WITH_ANSWER