Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
bartleby

Videos

Question
Book Icon
Chapter 3, Problem 11PT
To determine

To calculate: The solution set for the system of equations.

  x+y+z=4x+3y+3z=102x+y−z=3

Expert Solution & Answer
Check Mark

Answer to Problem 11PT

The solution set for the system of equations is (1,2,1) .

Explanation of Solution

Given information:

The system of equations

  x+y+z=4x+3y+3z=102x+y−z=3

Calculation:

Consider the system of equations

  x+y+z=4x+3y+3z=102x+y−z=3

Take the first and the second equation,

  x+y+z=4x+3y+3z=10

Use the method of elimination to solve the system above.

Subtract both the equations,

  x+y+z=4x+3y+3z=10−−2y−2z=−6

Simplify it further as,

  2y+2z=6y+z=3

Take the second and the third equation,

  x+3y+3z=102x+y−z=3

Multiply first equation by 2.

Use the method of elimination to solve the system above.

Subtract both the equations,

  2x+6y+6z=202x+y−z=3−5y+7z=17

Simplify it further as,

  5y+7z=17

Solve the system of equation 5y+7z=17 and y+z=3 .

Isolate the value of y from y+z=3 and substitute in 5y+7z=17 .

  5(3−z)+7z=172z=17−152z=2z=1

Substitute z=1 in the equation y+z=3 .

  y+1=3y=2

Now substitute z=1 and y=2 in the equation x+y+z=4 ,

  x+2+1=4x=1

Therefore, solution is the coordinate pair, (1,2,1) .

Thus, the solution set for the system of equations is

  (1,2,1) .

Previous
Chapter 3, Problem 10PT
Next
Chapter 3, Problem 12PT

Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2ACYPCh. 3.1 - Prob. 2BCYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYPCh. 3.1 - Prob. 4CCYPCh. 3.1 - Prob. 4DCYPCh. 3.1 - Prob. 1CYU
Ch. 3.1 - Prob. 2CYUCh. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - Prob. 5CYUCh. 3.1 - Prob. 6CYUCh. 3.1 - Prob. 7CYUCh. 3.1 - Prob. 8CYUCh. 3.1 - Prob. 9CYUCh. 3.1 - Prob. 10CYUCh. 3.1 - Prob. 11CYUCh. 3.1 - Prob. 12CYUCh. 3.1 - Prob. 13PPSCh. 3.1 - Prob. 14PPSCh. 3.1 - Prob. 15PPSCh. 3.1 - Prob. 16PPSCh. 3.1 - Prob. 17PPSCh. 3.1 - Prob. 18PPSCh. 3.1 - Prob. 19PPSCh. 3.1 - Prob. 20PPSCh. 3.1 - Prob. 21PPSCh. 3.1 - Prob. 22PPSCh. 3.1 - Prob. 23PPSCh. 3.1 - Prob. 24PPSCh. 3.1 - Prob. 25PPSCh. 3.1 - Prob. 26PPSCh. 3.1 - Prob. 27PPSCh. 3.1 - Prob. 28PPSCh. 3.1 - Prob. 29PPSCh. 3.1 - Prob. 30PPSCh. 3.1 - Prob. 31PPSCh. 3.1 - Prob. 32PPSCh. 3.1 - Prob. 33PPSCh. 3.1 - Prob. 34PPSCh. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 36PPSCh. 3.1 - Prob. 37PPSCh. 3.1 - Prob. 38PPSCh. 3.1 - Prob. 39PPSCh. 3.1 - Prob. 40PPSCh. 3.1 - Prob. 41PPSCh. 3.1 - Prob. 42HPCh. 3.1 - Prob. 43HPCh. 3.1 - Prob. 44HPCh. 3.1 - Prob. 45HPCh. 3.1 - Prob. 46HPCh. 3.1 - Prob. 47HPCh. 3.1 - Prob. 48HPCh. 3.1 - Prob. 49HPCh. 3.1 - Prob. 50HPCh. 3.1 - Prob. 51STPCh. 3.1 - Prob. 52STPCh. 3.1 - Prob. 53STPCh. 3.1 - Prob. 54STPCh. 3.1 - Prob. 55STPCh. 3.1 - Prob. 56STPCh. 3.1 - Prob. 57STPCh. 3.1 - Prob. 58STPCh. 3.1 - Prob. 59STPCh. 3.1 - Prob. 60STPCh. 3.1 - Prob. 61SCh. 3.1 - Prob. 62SCh. 3.1 - Prob. 63SCh. 3.1 - Prob. 64SCh. 3.1 - Prob. 65SCh. 3.1 - Prob. 66SCh. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.2 - Prob. 1ACYPCh. 3.2 - Prob. 1BCYPCh. 3.2 - Prob. 1CCYPCh. 3.2 - Prob. 2ACYPCh. 3.2 - Prob. 2BCYPCh. 3.2 - Prob. 2CCYPCh. 3.2 - Prob. 3CYPCh. 3.2 - Prob. 4ACYPCh. 3.2 - Prob. 4BCYPCh. 3.2 - Prob. 1CYUCh. 3.2 - Prob. 2CYUCh. 3.2 - Prob. 3CYUCh. 3.2 - Prob. 4CYUCh. 3.2 - Prob. 5CYUCh. 3.2 - Prob. 6CYUCh. 3.2 - Prob. 7CYUCh. 3.2 - Prob. 8CYUCh. 3.2 - Prob. 9CYUCh. 3.2 - Prob. 10CYUCh. 3.2 - Prob. 11CYUCh. 3.2 - Prob. 12CYUCh. 3.2 - Prob. 13CYUCh. 3.2 - Prob. 14CYUCh. 3.2 - Prob. 15PPSCh. 3.2 - Prob. 16PPSCh. 3.2 - Prob. 17PPSCh. 3.2 - Prob. 18PPSCh. 3.2 - Prob. 19PPSCh. 3.2 - Prob. 20PPSCh. 3.2 - Prob. 21PPSCh. 3.2 - Prob. 22PPSCh. 3.2 - Prob. 23PPSCh. 3.2 - Prob. 24PPSCh. 3.2 - Prob. 25PPSCh. 3.2 - Prob. 26PPSCh. 3.2 - Prob. 27PPSCh. 3.2 - Prob. 28PPSCh. 3.2 - Prob. 29PPSCh. 3.2 - Prob. 30PPSCh. 3.2 - Prob. 31PPSCh. 3.2 - Prob. 32PPSCh. 3.2 - Prob. 33PPSCh. 3.2 - Prob. 34PPSCh. 3.2 - Prob. 35PPSCh. 3.2 - Prob. 36PPSCh. 3.2 - Prob. 37PPSCh. 3.2 - Prob. 38PPSCh. 3.2 - Prob. 39PPSCh. 3.2 - Prob. 40PPSCh. 3.2 - Prob. 41PPSCh. 3.2 - Prob. 42PPSCh. 3.2 - Prob. 43PPSCh. 3.2 - Prob. 44PPSCh. 3.2 - Prob. 45PPSCh. 3.2 - Prob. 46PPSCh. 3.2 - Prob. 47PPSCh. 3.2 - Prob. 48PPSCh. 3.2 - Prob. 49PPSCh. 3.2 - Prob. 50PPSCh. 3.2 - Prob. 51PPSCh. 3.2 - Prob. 52PPSCh. 3.2 - Prob. 53PPSCh. 3.2 - Prob. 54PPSCh. 3.2 - Prob. 55PPSCh. 3.2 - Prob. 56PPSCh. 3.2 - Prob. 57PPSCh. 3.2 - Prob. 58PPSCh. 3.2 - Prob. 59PPSCh. 3.2 - Prob. 60PPSCh. 3.2 - Prob. 61PPSCh. 3.2 - Prob. 62PPSCh. 3.2 - Prob. 63PPSCh. 3.2 - Prob. 64HPCh. 3.2 - Prob. 65HPCh. 3.2 - Prob. 66HPCh. 3.2 - Prob. 67HPCh. 3.2 - Prob. 68HPCh. 3.2 - Prob. 69HPCh. 3.2 - Prob. 70HPCh. 3.2 - Prob. 71HPCh. 3.2 - Prob. 72HPCh. 3.2 - Prob. 73STPCh. 3.2 - Prob. 74STPCh. 3.2 - Prob. 75STPCh. 3.2 - Prob. 76STPCh. 3.2 - Prob. 77STPCh. 3.2 - Prob. 78STPCh. 3.2 - Prob. 79STPCh. 3.2 - Prob. 80STPCh. 3.2 - Prob. 81SCh. 3.2 - Prob. 82SCh. 3.2 - Prob. 83SCh. 3.3 - Prob. 1ACYPCh. 3.3 - Prob. 1BCYPCh. 3.3 - Prob. 2ACYPCh. 3.3 - Prob. 2BCYPCh. 3.3 - Prob. 3CYPCh. 3.3 - Prob. 4ACYPCh. 3.3 - Prob. 4BCYPCh. 3.3 - Prob. 1CYUCh. 3.3 - Prob. 2CYUCh. 3.3 - Prob. 3CYUCh. 3.3 - Prob. 4CYUCh. 3.3 - Prob. 5CYUCh. 3.3 - Prob. 6CYUCh. 3.3 - Prob. 7PPSCh. 3.3 - Prob. 8PPSCh. 3.3 - Prob. 9PPSCh. 3.3 - Prob. 10PPSCh. 3.3 - Prob. 11PPSCh. 3.3 - Prob. 12PPSCh. 3.3 - Prob. 13PPSCh. 3.3 - Prob. 14PPSCh. 3.3 - Prob. 15PPSCh. 3.3 - Prob. 16PPSCh. 3.3 - Prob. 17PPSCh. 3.3 - Prob. 18PPSCh. 3.3 - Prob. 19PPSCh. 3.3 - Prob. 20PPSCh. 3.3 - Prob. 21PPSCh. 3.3 - Prob. 22PPSCh. 3.3 - Prob. 23PPSCh. 3.3 - Prob. 24PPSCh. 3.3 - Prob. 25PPSCh. 3.3 - Prob. 26PPSCh. 3.3 - Prob. 27PPSCh. 3.3 - Prob. 28PPSCh. 3.3 - Prob. 29PPSCh. 3.3 - Prob. 30PPSCh. 3.3 - Prob. 31PPSCh. 3.3 - Prob. 32PPSCh. 3.3 - Prob. 33PPSCh. 3.3 - Prob. 34PPSCh. 3.3 - Prob. 35PPSCh. 3.3 - Prob. 36PPSCh. 3.3 - Prob. 37PPSCh. 3.3 - Prob. 38PPSCh. 3.3 - Prob. 39PPSCh. 3.3 - Prob. 40PPSCh. 3.3 - Prob. 41PPSCh. 3.3 - Prob. 42PPSCh. 3.3 - Prob. 43PPSCh. 3.3 - Prob. 44PPSCh. 3.3 - Prob. 45HPCh. 3.3 - Prob. 46HPCh. 3.3 - Prob. 47HPCh. 3.3 - Prob. 48HPCh. 3.3 - Prob. 49HPCh. 3.3 - Prob. 50HPCh. 3.3 - Prob. 51HPCh. 3.3 - Prob. 52HPCh. 3.3 - Prob. 53HPCh. 3.3 - Prob. 54HPCh. 3.3 - Prob. 55STPCh. 3.3 - Prob. 56STPCh. 3.3 - Prob. 57STPCh. 3.3 - Prob. 58STPCh. 3.3 - Prob. 59STPCh. 3.3 - Prob. 60STPCh. 3.3 - Prob. 61STPCh. 3.3 - Prob. 62STPCh. 3.3 - Prob. 63SCh. 3.3 - Prob. 64SCh. 3.3 - Prob. 65SCh. 3.3 - Prob. 66SCh. 3.3 - Prob. 67SCh. 3.3 - Prob. 68SCh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.4 - Prob. 1ACYPCh. 3.4 - Prob. 1BCYPCh. 3.4 - Prob. 2ACYPCh. 3.4 - Prob. 2BCYPCh. 3.4 - Prob. 3CYPCh. 3.4 - Prob. 1CYUCh. 3.4 - Prob. 2CYUCh. 3.4 - Prob. 3CYUCh. 3.4 - Prob. 4CYUCh. 3.4 - Prob. 5CYUCh. 3.4 - Prob. 6CYUCh. 3.4 - Prob. 7CYUCh. 3.4 - Prob. 8PPSCh. 3.4 - Prob. 9PPSCh. 3.4 - Prob. 10PPSCh. 3.4 - Prob. 11PPSCh. 3.4 - Prob. 12PPSCh. 3.4 - Prob. 13PPSCh. 3.4 - Prob. 14PPSCh. 3.4 - Prob. 15PPSCh. 3.4 - Prob. 16PPSCh. 3.4 - Prob. 17PPSCh. 3.4 - Prob. 18PPSCh. 3.4 - Prob. 19PPSCh. 3.4 - Prob. 20PPSCh. 3.4 - Prob. 21PPSCh. 3.4 - Prob. 22PPSCh. 3.4 - Prob. 23PPSCh. 3.4 - Prob. 24PPSCh. 3.4 - Prob. 25PPSCh. 3.4 - Prob. 26PPSCh. 3.4 - Prob. 27PPSCh. 3.4 - Prob. 28PPSCh. 3.4 - Prob. 29PPSCh. 3.4 - Prob. 30HPCh. 3.4 - Prob. 31HPCh. 3.4 - Prob. 32HPCh. 3.4 - Prob. 33HPCh. 3.4 - Prob. 34HPCh. 3.4 - Prob. 35HPCh. 3.4 - Prob. 36HPCh. 3.4 - Prob. 37HPCh. 3.4 - Prob. 38STPCh. 3.4 - Prob. 39STPCh. 3.4 - Prob. 40STPCh. 3.4 - Prob. 41STPCh. 3.4 - Prob. 42STPCh. 3.4 - Prob. 43STPCh. 3.4 - Prob. 44STPCh. 3.4 - Prob. 45STPCh. 3.4 - Prob. 46STPCh. 3.4 - Prob. 47STPCh. 3.4 - Prob. 48STPCh. 3.4 - Prob. 49STPCh. 3.4 - Prob. 50SCh. 3.4 - Prob. 51SCh. 3.4 - Prob. 52SCh. 3.4 - Prob. 53SCh. 3.4 - Prob. 54SCh. 3.4 - Prob. 55SCh. 3.5 - Prob. 1ACYPCh. 3.5 - Prob. 1BCYPCh. 3.5 - Prob. 2ACYPCh. 3.5 - Prob. 2BCYPCh. 3.5 - Prob. 3CYPCh. 3.5 - Prob. 1CYUCh. 3.5 - Prob. 2CYUCh. 3.5 - Prob. 3CYUCh. 3.5 - Prob. 4CYUCh. 3.5 - Prob. 5CYUCh. 3.5 - Prob. 6CYUCh. 3.5 - Prob. 7CYUCh. 3.5 - Prob. 8PPSCh. 3.5 - Prob. 9PPSCh. 3.5 - Prob. 10PPSCh. 3.5 - Prob. 11PPSCh. 3.5 - Prob. 12PPSCh. 3.5 - Prob. 13PPSCh. 3.5 - Prob. 14PPSCh. 3.5 - Prob. 15PPSCh. 3.5 - Prob. 16PPSCh. 3.5 - Prob. 17PPSCh. 3.5 - Prob. 18PPSCh. 3.5 - Prob. 19PPSCh. 3.5 - Prob. 20PPSCh. 3.5 - Prob. 21PPSCh. 3.5 - Prob. 22PPSCh. 3.5 - Prob. 23PPSCh. 3.5 - Prob. 24HPCh. 3.5 - Prob. 25HPCh. 3.5 - Prob. 26HPCh. 3.5 - Prob. 27HPCh. 3.5 - Prob. 28HPCh. 3.5 - Prob. 29HPCh. 3.5 - Prob. 30HPCh. 3.5 - Prob. 31HPCh. 3.5 - Prob. 32HPCh. 3.5 - Prob. 33HPCh. 3.5 - Prob. 34STPCh. 3.5 - Prob. 35STPCh. 3.5 - Prob. 36STPCh. 3.5 - Prob. 37STPCh. 3.5 - Prob. 38STPCh. 3.5 - Prob. 39SCh. 3.5 - Prob. 40SCh. 3.5 - Prob. 41SCh. 3.5 - Prob. 42SCh. 3 - Prob. 1QCCh. 3 - Prob. 2QCCh. 3 - Prob. 3QCCh. 3 - Prob. 4QCCh. 3 - Prob. 5QCCh. 3 - Prob. 6QCCh. 3 - Prob. 7QCCh. 3 - Prob. 8QCCh. 3 - Prob. 9QCCh. 3 - Prob. 10QCCh. 3 - Prob. 11QCCh. 3 - Prob. 12QCCh. 3 - Prob. 13QCCh. 3 - Prob. 14QCCh. 3 - Prob. 1MCQCh. 3 - Prob. 2MCQCh. 3 - Prob. 3MCQCh. 3 - Prob. 4MCQCh. 3 - Prob. 5MCQCh. 3 - Prob. 6MCQCh. 3 - Prob. 7MCQCh. 3 - Prob. 8MCQCh. 3 - Prob. 9MCQCh. 3 - Prob. 10MCQCh. 3 - Prob. 11MCQCh. 3 - Prob. 12MCQCh. 3 - Prob. 13MCQCh. 3 - Prob. 14MCQCh. 3 - Prob. 15MCQCh. 3 - Prob. 16MCQCh. 3 - Prob. 17MCQCh. 3 - Prob. 18MCQCh. 3 - Prob. 19MCQCh. 3 - Prob. 20MCQCh. 3 - Prob. 21MCQCh. 3 - Prob. 22MCQCh. 3 - Prob. 1SGRCh. 3 - Prob. 2SGRCh. 3 - Prob. 3SGRCh. 3 - Prob. 4SGRCh. 3 - Prob. 5SGRCh. 3 - Prob. 6SGRCh. 3 - Prob. 7SGRCh. 3 - Prob. 8SGRCh. 3 - Prob. 9SGRCh. 3 - Prob. 10SGRCh. 3 - Prob. 11SGRCh. 3 - Prob. 12SGRCh. 3 - Prob. 13SGRCh. 3 - Prob. 14SGRCh. 3 - Prob. 15SGRCh. 3 - Prob. 16SGRCh. 3 - Prob. 17SGRCh. 3 - Prob. 18SGRCh. 3 - Prob. 19SGRCh. 3 - Prob. 20SGRCh. 3 - Prob. 21SGRCh. 3 - Prob. 22SGRCh. 3 - Prob. 23SGRCh. 3 - Prob. 24SGRCh. 3 - Prob. 25SGRCh. 3 - Prob. 26SGRCh. 3 - Prob. 27SGRCh. 3 - Prob. 28SGRCh. 3 - Prob. 29SGRCh. 3 - Prob. 30SGRCh. 3 - Prob. 1PTCh. 3 - Prob. 2PTCh. 3 - Prob. 3PTCh. 3 - Prob. 4PTCh. 3 - Prob. 5PTCh. 3 - Prob. 6PTCh. 3 - Prob. 7PTCh. 3 - Prob. 8PTCh. 3 - Prob. 9PTCh. 3 - Prob. 10PTCh. 3 - Prob. 11PTCh. 3 - Prob. 12PTCh. 3 - Prob. 13PTCh. 3 - Prob. 14PTCh. 3 - Prob. 15PTCh. 3 - Prob. 16PTCh. 3 - Prob. 17PTCh. 3 - Prob. 18PTCh. 3 - Prob. 19PTCh. 3 - Prob. 1ECh. 3 - Prob. 2ECh. 3 - Prob. 3ECh. 3 - Prob. 4ECh. 3 - Prob. 1STPCh. 3 - Prob. 2STPCh. 3 - Prob. 3STPCh. 3 - Prob. 4STPCh. 3 - Prob. 5STPCh. 3 - Prob. 6STPCh. 3 - Prob. 7STPCh. 3 - Prob. 8STPCh. 3 - Prob. 9STPCh. 3 - Prob. 10STPCh. 3 - Prob. 11STPCh. 3 - Prob. 12STPCh. 3 - Prob. 13STP

Additional Math Textbook Solutions

Find more solutions based on key concepts
Factor the Greatest Common Factor from a Polynomial In the following exercises, factor the greatest common fact...

PREALGEBRA

Fill in each blanks so that the resulting statement is true. Any set of ordered pairs is called a/an _______. T...

College Algebra (7th Edition)

Complete the square to make a perfect square trinomial. Write the result as a binomial square. b24b

Elementary Algebra

Fill in each blanks so that the resulting statement is true. Any set of ordered pairs is called a/an _______. T...

College Algebra

Compute the determinants in Exercises 914 by a cofactor expansions. At each step, chose a row or column that in...

Linear Algebra and Its Applications (5th Edition)

Find the x- and y-intercepts of this equation, and sketch the graph of the line using just the intercepts plott...

College Algebra

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
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