Beginning & Intermediate Algebra (6th Edition)
Beginning & Intermediate Algebra (6th Edition)
6th Edition
ISBN: 9780134193090
Author: Elayn Martin-Gay
Publisher: PEARSON
Question
Book Icon
Chapter D, Problem 1P
To determine

To find:

The solutions of the system of equations.

x+4y=-2

3x-y=7

Expert Solution & Answer
Check Mark

Answer to Problem 1P

Solution:

x=2;y=-1

Explanation of Solution

1) Concept:

To solve a system of two equations in x and y using matrices:

Step 1. Write the corresponding matrix associated with the system of equations.

Step 2. Use elementary row operations to get equivalent matrix of the form:

1a01bc; where a,b,c are constants.

Step 3. Solve for x and y.

2) Calculation:

x+4y=-2

3x-y=7

The corresponding matrix associated with the above system of equations is

143-1-27

The element in (row1, column1) position is already 1.

To get the (row2, column1) position as zero, multiply row1 by -3 and add to row2:

14-31+3-34-1-2-3-2+7

Simplify further:

140-13-213

Use elementary row operation to get the (row2, column2) position as 1.

So, divide row 2 by -13

140-13-13-13-213-13

Simplify further,

1401-2-1

The above matrix corresponds to the system of equations:

x+4y=-2

y=-1

Substitute y=-1 in the first equation, x+4y=-2.

x+4-1=-2

x-4=-2

x=-2+4

x=2

Thus, the solutions of the given system of equations are: x=2;y=-1.

Conclusion:

Therefore, the required solutions are: x=2;y=-1.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Text book image
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
Text book image
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education