Skip to main content

Math Algebra ISE Intermediate Algebra

The given each system of equations To solve the system by the substitution method. Solution: The graphs of given system of equations are The given system is solved by using substitution method. The solution set of given system of equations { ( − 3 , 3 ) , ( 3 , 3 ) } Explanation: Given: The system of equations is x 2 + y 2 = 12 y = x 2 Calculation: The graphs of given system of equations are The point of intersection of graphs of two equations is the solution to the given system. Therefore, the solution set of given system of equations is { ( − 3 , 3 ) , ( 3 , 3 ) } Solving system by substitution method: Consider given system y = x 2 ------(1) x 2 + y 2 = 12 ------(2) Substitute eq--(1) in eq---(2) ⇒ x 2 + y 2 = 12 ⇒ x 2 + ( x 2 ) 2 = 12 ⇒ x 4 + x 2 − 12 = 0 ⇒ x 4 + 4 x 2 − 3 x 2 − 12 = 0 ⇒ x 2 ( x 2 + 4 ) − 3 ( x 2 + 4 ) = 0 ⇒ ( x 2 + 4 ) ( x 2 − 3 ) = 0 ( x 2 + 4 ) ≠ 0 ∴ x = ± 3 consider y = x 2 ------(1) for x = − 3 ⇒ y = ( − 3 ) 2 ⇒ y = 3 so ( − 3 , 3 ) is the solution for x = 3 ⇒ y = ( 3 ) 2 ⇒ y = 3 so ( 3 , 3 ) is the solution Therefore the solution set of given system of equations is { ( − 3 , 3 ) , ( 3 , 3 ) } Conclusion: The given each system of equations are drawn and solved by using substitution method. Hence, the solution set of given system of equations { ( − 3 , 3 ) , ( 3 , 3 ) }

The given each system of equations To solve the system by the substitution method. Solution: The graphs of given system of equations are The given system is solved by using substitution method. The solution set of given system of equations { ( − 3 , 3 ) , ( 3 , 3 ) } Explanation: Given: The system of equations is x 2 + y 2 = 12 y = x 2 Calculation: The graphs of given system of equations are The point of intersection of graphs of two equations is the solution to the given system. Therefore, the solution set of given system of equations is { ( − 3 , 3 ) , ( 3 , 3 ) } Solving system by substitution method: Consider given system y = x 2 ------(1) x 2 + y 2 = 12 ------(2) Substitute eq--(1) in eq---(2) ⇒ x 2 + y 2 = 12 ⇒ x 2 + ( x 2 ) 2 = 12 ⇒ x 4 + x 2 − 12 = 0 ⇒ x 4 + 4 x 2 − 3 x 2 − 12 = 0 ⇒ x 2 ( x 2 + 4 ) − 3 ( x 2 + 4 ) = 0 ⇒ ( x 2 + 4 ) ( x 2 − 3 ) = 0 ( x 2 + 4 ) ≠ 0 ∴ x = ± 3 consider y = x 2 ------(1) for x = − 3 ⇒ y = ( − 3 ) 2 ⇒ y = 3 so ( − 3 , 3 ) is the solution for x = 3 ⇒ y = ( 3 ) 2 ⇒ y = 3 so ( 3 , 3 ) is the solution Therefore the solution set of given system of equations is { ( − 3 , 3 ) , ( 3 , 3 ) } Conclusion: The given each system of equations are drawn and solved by using substitution method. Hence, the solution set of given system of equations { ( − 3 , 3 ) , ( 3 , 3 ) }

ISE Intermediate Algebra

ISE Intermediate Algebra

6th Edition

ISBN: 9781264418756

Author: Miller, Julie, O'Neill, Molly, Hyde, Nancy

Publisher: McGraw Hill

See similar textbooks

Videos

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

Blurred answer

Chapter 9.4, Problem 13PE

Chapter 9.4, Problem 15PE

Chapter 9 Solutions

ISE Intermediate Algebra

Ch. 9.1 - Prob. 1PE Ch. 9.1 - Prob. 2PE Ch. 9.1 - Prob. 3PE Ch. 9.1 - Prob. 4PE Ch. 9.1 - Prob. 5PE Ch. 9.1 - Prob. 6PE Ch. 9.1 - Prob. 7PE Ch. 9.1 - Prob. 8PE Ch. 9.1 - Prob. 9PE Ch. 9.1 - Prob. 10PE

Ch. 9.1 - Prob. 11PE Ch. 9.1 - Prob. 12PE Ch. 9.1 - Prob. 13PE Ch. 9.1 - Prob. 14PE Ch. 9.1 - Prob. 15PE Ch. 9.1 - Prob. 16PE Ch. 9.1 - Prob. 17PE Ch. 9.1 - Prob. 18PE Ch. 9.1 - Prob. 19PE Ch. 9.1 - Prob. 20PE Ch. 9.1 - Prob. 21PE Ch. 9.1 - Prob. 22PE Ch. 9.1 - Prob. 23PE Ch. 9.1 - Prob. 24PE Ch. 9.1 - Prob. 25PE Ch. 9.1 - Prob. 26PE Ch. 9.1 - Prob. 27PE Ch. 9.1 - Prob. 28PE Ch. 9.1 - Prob. 29PE Ch. 9.1 - Prob. 30PE Ch. 9.1 - Prob. 31PE Ch. 9.1 - Prob. 32PE Ch. 9.1 - Prob. 33PE Ch. 9.1 - Prob. 34PE Ch. 9.1 - Prob. 35PE Ch. 9.1 - Prob. 36PE Ch. 9.1 - Prob. 37PE Ch. 9.1 - Prob. 38PE Ch. 9.1 - Prob. 39PE Ch. 9.1 - Prob. 40PE Ch. 9.1 - Prob. 41PE Ch. 9.1 - Prob. 42PE Ch. 9.1 - Prob. 43PE Ch. 9.1 - Prob. 44PE Ch. 9.1 - Prob. 45PE Ch. 9.1 - Prob. 46PE Ch. 9.1 - Prob. 47PE Ch. 9.1 - Prob. 48PE Ch. 9.1 - Prob. 49PE Ch. 9.1 - Prob. 50PE Ch. 9.1 - Prob. 51PE Ch. 9.1 - Prob. 52PE Ch. 9.1 - Prob. 53PE Ch. 9.1 - Prob. 54PE Ch. 9.1 - Prob. 55PE Ch. 9.1 - Prob. 56PE Ch. 9.1 - Prob. 57PE Ch. 9.1 - Prob. 58PE Ch. 9.1 - Prob. 59PE Ch. 9.1 - Prob. 60PE Ch. 9.1 - Prob. 61PE Ch. 9.1 - Prob. 62PE Ch. 9.1 - Prob. 63PE Ch. 9.1 - Prob. 64PE Ch. 9.1 - Prob. 65PE Ch. 9.1 - Prob. 66PE Ch. 9.1 - Prob. 67PE Ch. 9.1 - Prob. 68PE Ch. 9.1 - Prob. 69PE Ch. 9.1 - Prob. 70PE Ch. 9.1 - Prob. 71PE Ch. 9.1 - Prob. 72PE Ch. 9.1 - Prob. 73PE Ch. 9.1 - Prob. 74PE Ch. 9.1 - Prob. 75PE Ch. 9.1 - Prob. 76PE Ch. 9.1 - Prob. 77PE Ch. 9.1 - Prob. 78PE Ch. 9.1 - Prob. 79PE Ch. 9.1 - Prob. 80PE Ch. 9.1 - Prob. 81PE Ch. 9.1 - Prob. 82PE Ch. 9.1 - Prob. 83PE Ch. 9.1 - Prob. 84PE Ch. 9.1 - Prob. 85PE Ch. 9.1 - Prob. 86PE Ch. 9.1 - Prob. 87PE Ch. 9.1 - Prob. 88PE Ch. 9.2 - Prob. 1PE Ch. 9.2 - Prob. 3PE Ch. 9.2 - Prob. 4PE Ch. 9.2 - Prob. 5PE Ch. 9.2 - Prob. 6PE Ch. 9.2 - For Exercises 9-16, use the equation of the...Ch. 9.2 - Prob. 8PE Ch. 9.2 - Prob. 9PE Ch. 9.2 - Prob. 10PE Ch. 9.2 - Prob. 11PE Ch. 9.2 - Prob. 12PE Ch. 9.2 - Prob. 13PE Ch. 9.2 - Prob. 14PE Ch. 9.2 - Prob. 15PE Ch. 9.2 - Prob. 16PE Ch. 9.2 - Prob. 17PE Ch. 9.2 - Prob. 18PE Ch. 9.2 - Prob. 19PE Ch. 9.2 - Prob. 20PE Ch. 9.2 - Prob. 21PE Ch. 9.2 - Prob. 22PE Ch. 9.2 - Prob. 23PE Ch. 9.2 - Prob. 24PE Ch. 9.2 - Prob. 25PE Ch. 9.2 - Prob. 26PE Ch. 9.2 - Prob. 27PE Ch. 9.2 - Prob. 28PE Ch. 9.2 - Prob. 29PE Ch. 9.2 - Prob. 30PE Ch. 9.2 - Prob. 31PE Ch. 9.2 - Prob. 32PE Ch. 9.2 - Prob. 33PE Ch. 9.2 - Prob. 34PE Ch. 9.2 - Prob. 35PE Ch. 9.2 - Prob. 36PE Ch. 9.2 - Prob. 37PE Ch. 9.2 - Prob. 38PE Ch. 9.2 - Prob. 39PE Ch. 9.2 - Prob. 40PE Ch. 9.2 - Prob. 41PE Ch. 9.2 - Prob. 42PE Ch. 9.2 - Prob. 43PE Ch. 9.3 - Prob. 3PE Ch. 9.3 - Prob. 4PE Ch. 9.3 - Prob. 5PE Ch. 9.3 - Prob. 6PE Ch. 9.3 - Prob. 7PE Ch. 9.3 - Prob. 8PE Ch. 9.3 - Prob. 9PE Ch. 9.3 - Prob. 10PE Ch. 9.3 - Prob. 11PE Ch. 9.3 - Prob. 12PE Ch. 9.3 - Prob. 13PE Ch. 9.3 - Prob. 14PE Ch. 9.3 - Prob. 15PE Ch. 9.3 - Prob. 16PE Ch. 9.3 - Prob. 17PE Ch. 9.3 - Prob. 18PE Ch. 9.3 - Prob. 19PE Ch. 9.3 - Prob. 20PE Ch. 9.3 - Prob. 21PE Ch. 9.3 - Prob. 22PE Ch. 9.3 - Prob. 23PE Ch. 9.3 - Prob. 24PE Ch. 9.3 - Prob. 25PE Ch. 9.3 - Prob. 26PE Ch. 9.3 - Prob. 27PE Ch. 9.3 - Prob. 28PE Ch. 9.3 - Prob. 29PE Ch. 9.3 - Prob. 30PE Ch. 9.3 - Prob. 31PE Ch. 9.3 - Prob. 32PE Ch. 9.3 - Prob. 33PE Ch. 9.3 - Prob. 34PE Ch. 9.3 - Prob. 35PE Ch. 9.3 - Prob. 36PE Ch. 9.3 - Prob. 37PE Ch. 9.3 - Prob. 38PE Ch. 9.3 - Prob. 39PE Ch. 9.3 - Prob. 40PE Ch. 9.3 - Prob. 41PE Ch. 9.3 - Prob. 42PE Ch. 9.3 - Prob. 43PE Ch. 9.3 - Prob. 44PE Ch. 9.3 - Prob. 45PE Ch. 9.3 - Prob. 46PE Ch. 9.3 - Prob. 47PE Ch. 9.3 - Prob. 48PE Ch. 9.3 - Prob. 49PE Ch. 9.3 - Prob. 50PE Ch. 9.3 - Prob. 51PE Ch. 9.3 - Prob. 52PE Ch. 9.3 - Prob. 1PRE Ch. 9.3 - Prob. 2PRE Ch. 9.3 - Prob. 3PRE Ch. 9.3 - Prob. 4PRE Ch. 9.3 - Prob. 5PRE Ch. 9.3 - Prob. 6PRE Ch. 9.3 - Prob. 7PRE Ch. 9.3 - Prob. 8PRE Ch. 9.3 - Prob. 9PRE Ch. 9.3 - Prob. 10PRE Ch. 9.3 - Prob. 11PRE Ch. 9.3 - Prob. 12PRE Ch. 9.3 - Prob. 13PRE Ch. 9.3 - Prob. 14PRE Ch. 9.3 - Prob. 15PRE Ch. 9.3 - Prob. 16PRE Ch. 9.3 - Prob. 17PRE Ch. 9.3 - Prob. 18PRE Ch. 9.3 - Prob. 19PRE Ch. 9.3 - Prob. 20PRE Ch. 9.3 - Prob. 21PRE Ch. 9.3 - Prob. 22PRE Ch. 9.3 - Prob. 23PRE Ch. 9.3 - Prob. 24PRE Ch. 9.3 - Prob. 25PRE Ch. 9.3 - Prob. 26PRE Ch. 9.3 - Prob. 27PRE Ch. 9.3 - Prob. 28PRE Ch. 9.3 - Prob. 29PRE Ch. 9.3 - Prob. 30PRE Ch. 9.4 - Prob. 1PE Ch. 9.4 - Prob. 2PE Ch. 9.4 - Prob. 3PE Ch. 9.4 - Prob. 4PE Ch. 9.4 - Prob. 5PE Ch. 9.4 - Prob. 6PE Ch. 9.4 - Prob. 7PE Ch. 9.4 - Prob. 8PE Ch. 9.4 - Prob. 9PE Ch. 9.4 - Prob. 10PE Ch. 9.4 - Prob. 11PE Ch. 9.4 - Prob. 12PE Ch. 9.4 - Prob. 13PE Ch. 9.4 - Prob. 14PE Ch. 9.4 - Prob. 15PE Ch. 9.4 - Prob. 16PE Ch. 9.4 - Prob. 17PE Ch. 9.4 - Prob. 18PE Ch. 9.4 - Prob. 19PE Ch. 9.4 - Prob. 20PE Ch. 9.4 - Prob. 21PE Ch. 9.4 - Prob. 22PE Ch. 9.4 - Prob. 23PE Ch. 9.4 - Prob. 24PE Ch. 9.4 - Prob. 25PE Ch. 9.4 - Prob. 26PE Ch. 9.4 - Prob. 27PE Ch. 9.4 - Prob. 28PE Ch. 9.4 - Prob. 29PE Ch. 9.4 - Prob. 30PE Ch. 9.4 - Prob. 31PE Ch. 9.4 - Prob. 32PE Ch. 9.4 - Prob. 33PE Ch. 9.4 - Prob. 34PE Ch. 9.4 - Prob. 35PE Ch. 9.4 - Prob. 36PE Ch. 9.4 - Prob. 37PE Ch. 9.4 - Prob. 38PE Ch. 9.4 - Prob. 39PE Ch. 9.4 - Prob. 40PE Ch. 9.5 - Prob. 1PE Ch. 9.5 - Prob. 2PE Ch. 9.5 - Prob. 3PE Ch. 9.5 - Prob. 4PE Ch. 9.5 - Prob. 5PE Ch. 9.5 - Prob. 6PE Ch. 9.5 - Prob. 7PE Ch. 9.5 - Prob. 8PE Ch. 9.5 - Prob. 9PE Ch. 9.5 - Prob. 10PE Ch. 9.5 - Prob. 11PE Ch. 9.5 - Prob. 12PE Ch. 9.5 - Prob. 13PE Ch. 9.5 - Prob. 14PE Ch. 9.5 - Prob. 15PE Ch. 9.5 - Prob. 16PE Ch. 9.5 - Prob. 17PE Ch. 9.5 - Prob. 18PE Ch. 9.5 - Prob. 19PE Ch. 9.5 - Prob. 20PE Ch. 9.5 - Prob. 21PE Ch. 9.5 - Prob. 22PE Ch. 9.5 - Prob. 23PE Ch. 9.5 - Prob. 24PE Ch. 9.5 - Prob. 25PE Ch. 9.5 - Prob. 26PE Ch. 9.5 - Prob. 27PE Ch. 9.5 - Prob. 28PE Ch. 9.5 - Prob. 29PE Ch. 9.5 - Prob. 30PE Ch. 9.5 - Prob. 31PE Ch. 9.5 - Prob. 32PE Ch. 9.5 - Prob. 33PE Ch. 9.5 - Prob. 34PE Ch. 9.5 - Prob. 35PE Ch. 9.5 - Prob. 36PE Ch. 9.5 - Prob. 37PE Ch. 9.5 - Prob. 38PE Ch. 9.5 - Prob. 39PE Ch. 9.5 - Prob. 40PE Ch. 9.5 - Prob. 41PE Ch. 9.5 - Prob. 42PE Ch. 9.5 - Prob. 43PE Ch. 9 - Prob. 1RE Ch. 9 - For Exercises 1—2, find the distance between the...Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Prob. 28RE Ch. 9 - Prob. 29RE Ch. 9 - Prob. 30RE Ch. 9 - Prob. 31RE Ch. 9 - Prob. 32RE Ch. 9 - Prob. 33RE Ch. 9 - Prob. 34RE Ch. 9 - Prob. 35RE Ch. 9 - Prob. 36RE Ch. 9 - Prob. 37RE Ch. 9 - Prob. 38RE Ch. 9 - Prob. 39RE Ch. 9 - Prob. 40RE Ch. 9 - Prob. 41RE Ch. 9 - Prob. 42RE Ch. 9 - Prob. 43RE Ch. 9 - Prob. 44RE Ch. 9 - Prob. 45RE Ch. 9 - Prob. 46RE Ch. 9 - Prob. 47RE Ch. 9 - Prob. 48RE Ch. 9 - Prob. 49RE Ch. 9 - Prob. 50RE Ch. 9 - Prob. 51RE Ch. 9 - Prob. 52RE Ch. 9 - Prob. 53RE Ch. 9 - Prob. 54RE Ch. 9 - Prob. 55RE Ch. 9 - Prob. 56RE Ch. 9 - Prob. 57RE Ch. 9 - Prob. 58RE Ch. 9 - Prob. 59RE Ch. 9 - Prob. 60RE Ch. 9 - Prob. 61RE Ch. 9 - Prob. 1T Ch. 9 - Prob. 2T Ch. 9 - Prob. 3T Ch. 9 - Prob. 4T Ch. 9 - Find the center of the circle that has a diameter...Ch. 9 - Prob. 6T Ch. 9 - Prob. 7T Ch. 9 - Prob. 8T Ch. 9 - Prob. 9T Ch. 9 - Prob. 10T Ch. 9 - Prob. 11T Ch. 9 - Prob. 12T Ch. 9 - Prob. 13T Ch. 9 - Prob. 14T Ch. 9 - Prob. 15T Ch. 9 - Prob. 16T Ch. 9 - Prob. 17T Ch. 9 - Prob. 18T

Knowledge Booster

Background pattern image

$Algebra$

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.

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 (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

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

SEE MORE TEXTBOOKS

UG/ linear equation in linear algebra; Author: The Gate Academy;https://www.youtube.com/watch?v=aN5ezoOXX5A;License: Standard YouTube License, CC-BY

System of Linear Equations-I; Author: IIT Roorkee July 2018;https://www.youtube.com/watch?v=HOXWRNuH3BE;License: Standard YouTube License, CC-BY