need help # Solving Systems of EquationsTwo systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution.## System 1:\[-x - 2y = -2\]\[x + 2y = 2\]- ○ The system has no solution.- ⊙ The system has a unique solution: $(x, y) = ( \_ , \_ )$- ○ The system has infinitely many solutions. They must satisfy the following equation: $y = \_$Solution: The indicated answer for this system is that it has no solution.## System 2:\[x + 2y = 6\]\[-x - 2y = 6\]- ⊙ The system has no solution.- ○ The system has a unique solution: $(x, y) = ( \_ , \_ )$- ○ The system has infinitely many solutions. They must satisfy the following equation: $y = \_$Solution: The indicated answer for this system is that it has a unique solution.

Answered: need help

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,...

See similar textbooks

Related questions

Concept explainers

Question

need help

# Solving Systems of Equations

Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution.

## System 1:

\[
-x - 2y = -2
\]
\[
x + 2y = 2
\]

- ○ The system has no solution.
- ⊙ The system has a unique solution: $(x, y) = ( \_ , \_ )$
- ○ The system has infinitely many solutions. They must satisfy the following equation: $y = \_$

Solution: The indicated answer for this system is that it has no solution.

## System 2:

\[
x + 2y = 6
\]
\[
-x - 2y = 6
\]

- ⊙ The system has no solution.
- ○ The system has a unique solution: $(x, y) = ( \_ , \_ )$
- ○ The system has infinitely many solutions. They must satisfy the following equation: $y = \_$

Solution: The indicated answer for this system is that it has a unique solution.

Expert Solution

Step 1

$(1)$ The given equations are :

$- x - 2 y = - 2 x + 2 y = 2$

To find the solution of the equation ,

The coefficient in equation $1$ are ,

$a_{1} = - 1, b_{1} = - 2, c_{1} = - 2$

The coefficient in equation $2$ are ,

$a_{2} = 1, b_{2} = 2, c_{2} = 2$

Comparing the coefficient of the two equations ,

$\frac{a_{1}}{a_{2}} = \frac{- 1}{1} = - 1 \frac{b_{1}}{b_{2}} = \frac{- 2}{2} = - 1 \frac{c_{1}}{c_{2}} = \frac{- 2}{2} = - 1$

Hence , $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Thus, the system of equation has the infinitely many solutions.

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

help with these
Need Help Please

Recommended textbooks for you

Algebra and Trigonometry (6th Edition)

Algebra

ISBN:

9780134463216

Author:

Robert F. Blitzer

Publisher:

PEARSON

Contemporary Abstract Algebra

Algebra

ISBN:

9781305657960

Author:

Joseph Gallian

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra and Trigonometry (6th Edition)

Algebra

ISBN:

9780134463216

Author:

Robert F. Blitzer

Publisher:

PEARSON

Contemporary Abstract Algebra

Algebra

ISBN:

9781305657960

Author:

Joseph Gallian

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra And Trigonometry (11th Edition)

Algebra

ISBN:

9780135163078

Author:

Michael Sullivan

Publisher:

PEARSON

Introduction to Linear Algebra, Fifth Edition

Algebra

ISBN:

9780980232776

Author:

Gilbert Strang

Publisher:

Wellesley-Cambridge Press

College Algebra (Collegiate Math)

Algebra

ISBN:

9780077836344

Author:

Julie Miller, Donna Gerken

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS