High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
15th Edition
ISBN: 9780133281163
Author: Prentice Hall
Publisher: Prentice Hall
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Expert Solution & Answer
Chapter 3.5, Problem 18PPSE
Solution
To state: The solutions for the system of equation by elimination also check the answer.
{x+2y=22x+3y−z=−94x+2y+5z=1
The resultant solution is (−12211,7211,7111) .
Given information:
The given system equations is:
{x+2y=22x+3y−z=−94x+2y+5z=1
Explanation:
Write the original system equations:
{x+2y=22x+3y−z=−94x+2y+5z=1
Let’s number the equation,
{x+2y=2⋯(1)2x+3y−z=−9⋯(2)4x+2y+5z=1⋯(3)
Multiply equation (2) by -5,
(2x+3y−z=−9)×510x+15y−5z=−45⋯(4)
Add equations (3) and (4) to eliminate variable z ,
{4x+2y+5z=110x+15y−5z=−45¯14x+17y=−44
Number the resultant equation,
14x+17y=−44⋯(4)
Now multiply equation (1) by -14,
(x+2y=2)×−14−14x−28y=−28⋯(5)
Add equation (4) and (5) to eliminate variable x ,
{−14x−28y=−2814x+17y=−44¯ −11y=−72y=7211
Now find the value of variable x by substituting the value of y in equation (1) and simplify,
x+2y=2x+2(7211)=2x=2−14411x=22−14411x=−12211
Now find the value of variable z by substituting the values of x and y in equation (2) and simplify,
2x+3y−z=−92(−12211)+3(7211)−z=−9−24411+21611−z=−9−2811−z=−9−z=−9+2811−z=−7111z=7111
Therefore, the solution for the given system of equation is (−12211,7211,7111) .
Now check the solution by substituting the values of variables x , y and z into the other two original equations,
x+2y=2(−12211)+2(7211)?=2−122+14411?=22211?=22=2
Similarly substitute values of variables x , y and z into equation (3),
4x+2y+5z=14(−12211)+2(7211)+5(7111)?=1−48811+14411+35511?=1−488+144+35511?=11111?=11=1
Chapter 3 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
Ch. 3.1 - Prob. 1LCCh. 3.1 - Prob. 2LCCh. 3.1 - Prob. 3LCCh. 3.1 - Prob. 4LCCh. 3.1 - Prob. 5LCCh. 3.1 - Prob. 6LCCh. 3.1 - Prob. 7PPSECh. 3.1 - Prob. 8PPSECh. 3.1 - Prob. 9PPSECh. 3.1 - Prob. 10PPSE
Ch. 3.1 - Prob. 11PPSECh. 3.1 - Prob. 12PPSECh. 3.1 - Prob. 13PPSECh. 3.1 - Prob. 14PPSECh. 3.1 - Prob. 15PPSECh. 3.1 - Prob. 16PPSECh. 3.1 - Prob. 17PPSECh. 3.1 - Prob. 18PPSECh. 3.1 - Prob. 19PPSECh. 3.1 - Prob. 20PPSECh. 3.1 - Prob. 21PPSECh. 3.1 - Prob. 22PPSECh. 3.1 - Prob. 23PPSECh. 3.1 - Prob. 24PPSECh. 3.1 - Prob. 25PPSECh. 3.1 - Prob. 26PPSECh. 3.1 - Prob. 27PPSECh. 3.1 - Prob. 28PPSECh. 3.1 - Prob. 29PPSECh. 3.1 - Prob. 30PPSECh. 3.1 - Prob. 31PPSECh. 3.1 - Prob. 32PPSECh. 3.1 - Prob. 33PPSECh. 3.1 - Prob. 34PPSECh. 3.1 - Prob. 35PPSECh. 3.1 - Prob. 36PPSECh. 3.1 - Prob. 37PPSECh. 3.1 - Prob. 38PPSECh. 3.1 - Prob. 39PPSECh. 3.1 - Prob. 40PPSECh. 3.1 - Prob. 41PPSECh. 3.1 - Prob. 42PPSECh. 3.1 - Prob. 43PPSECh. 3.1 - Prob. 44PPSECh. 3.1 - Prob. 45PPSECh. 3.1 - Prob. 46PPSECh. 3.1 - Prob. 47PPSECh. 3.1 - Prob. 48PPSECh. 3.1 - Prob. 49PPSECh. 3.1 - Prob. 50PPSECh. 3.1 - Prob. 51PPSECh. 3.1 - Prob. 52PPSECh. 3.1 - Prob. 53PPSECh. 3.1 - Prob. 54PPSECh. 3.1 - Prob. 55PPSECh. 3.1 - Prob. 56PPSECh. 3.2 - Prob. 1LCCh. 3.2 - Prob. 2LCCh. 3.2 - Prob. 3LCCh. 3.2 - Prob. 4LCCh. 3.2 - Prob. 5LCCh. 3.2 - Prob. 6LCCh. 3.2 - Prob. 7LCCh. 3.2 - Prob. 8LCCh. 3.2 - Prob. 9LCCh. 3.2 - Prob. 10PPSECh. 3.2 - Prob. 11PPSECh. 3.2 - Prob. 12PPSECh. 3.2 - Prob. 13PPSECh. 3.2 - Prob. 14PPSECh. 3.2 - Prob. 15PPSECh. 3.2 - Prob. 16PPSECh. 3.2 - Prob. 17PPSECh. 3.2 - Prob. 18PPSECh. 3.2 - Prob. 19PPSECh. 3.2 - Prob. 20PPSECh. 3.2 - Prob. 21PPSECh. 3.2 - Prob. 22PPSECh. 3.2 - Prob. 23PPSECh. 3.2 - Prob. 24PPSECh. 3.2 - Prob. 25PPSECh. 3.2 - Prob. 26PPSECh. 3.2 - Prob. 27PPSECh. 3.2 - Prob. 28PPSECh. 3.2 - Prob. 29PPSECh. 3.2 - Prob. 30PPSECh. 3.2 - Prob. 31PPSECh. 3.2 - Prob. 32PPSECh. 3.2 - Prob. 33PPSECh. 3.2 - Prob. 34PPSECh. 3.2 - Prob. 35PPSECh. 3.2 - Prob. 36PPSECh. 3.2 - Prob. 37PPSECh. 3.2 - Prob. 38PPSECh. 3.2 - Prob. 39PPSECh. 3.2 - Prob. 40PPSECh. 3.2 - Prob. 41PPSECh. 3.2 - Prob. 42PPSECh. 3.2 - Prob. 43PPSECh. 3.2 - Prob. 44PPSECh. 3.2 - Prob. 45PPSECh. 3.2 - Prob. 46PPSECh. 3.2 - Prob. 47PPSECh. 3.2 - Prob. 48PPSECh. 3.2 - Prob. 49PPSECh. 3.2 - Prob. 50PPSECh. 3.2 - Prob. 51PPSECh. 3.2 - Prob. 52PPSECh. 3.2 - Prob. 53PPSECh. 3.2 - Prob. 54PPSECh. 3.2 - Prob. 55PPSECh. 3.2 - Prob. 56PPSECh. 3.2 - Prob. 57PPSECh. 3.2 - Prob. 58PPSECh. 3.2 - Prob. 59PPSECh. 3.2 - Prob. 60PPSECh. 3.2 - Prob. 61PPSECh. 3.2 - Prob. 62PPSECh. 3.2 - Prob. 63PPSECh. 3.2 - Prob. 64PPSECh. 3.2 - Prob. 65PPSECh. 3.2 - Prob. 66PPSECh. 3.2 - Prob. 67PPSECh. 3.2 - Prob. 68PPSECh. 3.2 - Prob. 69PPSECh. 3.2 - Prob. 70PPSECh. 3.2 - Prob. 71PPSECh. 3.3 - Prob. 1LCCh. 3.3 - Prob. 2LCCh. 3.3 - Prob. 3LCCh. 3.3 - Prob. 4LCCh. 3.3 - Prob. 5LCCh. 3.3 - Prob. 6LCCh. 3.3 - Prob. 7LCCh. 3.3 - Prob. 8PPSECh. 3.3 - Prob. 9PPSECh. 3.3 - Prob. 10PPSECh. 3.3 - Prob. 11PPSECh. 3.3 - Prob. 12PPSECh. 3.3 - Prob. 13PPSECh. 3.3 - Prob. 14PPSECh. 3.3 - Prob. 15PPSECh. 3.3 - Prob. 16PPSECh. 3.3 - Prob. 17PPSECh. 3.3 - Prob. 18PPSECh. 3.3 - Prob. 19PPSECh. 3.3 - Prob. 20PPSECh. 3.3 - Prob. 21PPSECh. 3.3 - Prob. 22PPSECh. 3.3 - Prob. 23PPSECh. 3.3 - Prob. 24PPSECh. 3.3 - Prob. 25PPSECh. 3.3 - Prob. 26PPSECh. 3.3 - Prob. 27PPSECh. 3.3 - Prob. 28PPSECh. 3.3 - Prob. 29PPSECh. 3.3 - Prob. 30PPSECh. 3.3 - Prob. 31PPSECh. 3.3 - Prob. 32PPSECh. 3.3 - Prob. 33PPSECh. 3.3 - Prob. 34PPSECh. 3.3 - Prob. 35PPSECh. 3.3 - Prob. 36PPSECh. 3.3 - Prob. 37PPSECh. 3.3 - Prob. 38PPSECh. 3.3 - Prob. 39PPSECh. 3.3 - Prob. 40PPSECh. 3.3 - Prob. 41PPSECh. 3.3 - Prob. 42PPSECh. 3.3 - Prob. 43PPSECh. 3.3 - Prob. 44PPSECh. 3.3 - Prob. 45PPSECh. 3.3 - Prob. 46PPSECh. 3.3 - Prob. 47PPSECh. 3.3 - Prob. 48PPSECh. 3.3 - Prob. 49PPSECh. 3.3 - Prob. 50PPSECh. 3.3 - Prob. 51PPSECh. 3.3 - Prob. 52PPSECh. 3.3 - Prob. 53PPSECh. 3.3 - Prob. 54PPSECh. 3.3 - Prob. 55PPSECh. 3.3 - Prob. 56PPSECh. 3.3 - Prob. 57PPSECh. 3.3 - Prob. 58PPSECh. 3.3 - Prob. 59PPSECh. 3.3 - Prob. 60PPSECh. 3.3 - Prob. 61PPSECh. 3.3 - Prob. 62PPSECh. 3.3 - Prob. 63PPSECh. 3.3 - Prob. 64PPSECh. 3.3 - Prob. 65PPSECh. 3.3 - Prob. 66PPSECh. 3.3 - Prob. 67PPSECh. 3.3 - Prob. 68PPSECh. 3.3 - Prob. 69PPSECh. 3.3 - Prob. 70PPSECh. 3.3 - Prob. 71PPSECh. 3.3 - Prob. 72PPSECh. 3.4 - Prob. 1LCCh. 3.4 - Prob. 2LCCh. 3.4 - Prob. 3LCCh. 3.4 - Prob. 4LCCh. 3.4 - Prob. 5LCCh. 3.4 - Prob. 6LCCh. 3.4 - Prob. 7LCCh. 3.4 - Prob. 8LCCh. 3.4 - Prob. 9LCCh. 3.4 - Prob. 10PPSECh. 3.4 - Prob. 11PPSECh. 3.4 - Prob. 12PPSECh. 3.4 - Prob. 13PPSECh. 3.4 - Prob. 14PPSECh. 3.4 - Prob. 15PPSECh. 3.4 - Prob. 16PPSECh. 3.4 - Prob. 17PPSECh. 3.4 - Prob. 18PPSECh. 3.4 - Prob. 19PPSECh. 3.4 - Prob. 20PPSECh. 3.4 - Prob. 21PPSECh. 3.4 - Prob. 22PPSECh. 3.4 - Prob. 23PPSECh. 3.4 - Prob. 24PPSECh. 3.4 - Prob. 25PPSECh. 3.4 - Prob. 26PPSECh. 3.4 - Prob. 27PPSECh. 3.4 - Prob. 28PPSECh. 3.4 - Prob. 29PPSECh. 3.4 - Prob. 30PPSECh. 3.4 - Prob. 31PPSECh. 3.4 - Prob. 32PPSECh. 3.4 - Prob. 33PPSECh. 3.4 - Prob. 34PPSECh. 3.4 - Prob. 35PPSECh. 3.4 - Prob. 36PPSECh. 3.4 - Prob. 37PPSECh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.5 - Prob. 1ACh. 3.5 - Prob. 2ACh. 3.5 - Prob. 3ACh. 3.5 - Prob. 4ACh. 3.5 - Prob. 5ACh. 3.5 - Prob. 6ACh. 3.5 - Prob. 7ACh. 3.5 - Prob. 8ACh. 3.5 - Prob. 9ACh. 3.5 - Prob. 10ACh. 3.5 - Prob. 11ACh. 3.5 - Prob. 12ECh. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 1LCCh. 3.5 - Prob. 2LCCh. 3.5 - Prob. 3LCCh. 3.5 - Prob. 4LCCh. 3.5 - Prob. 5LCCh. 3.5 - Prob. 6LCCh. 3.5 - Prob. 7LCCh. 3.5 - Prob. 8LCCh. 3.5 - Prob. 9PPSECh. 3.5 - Prob. 10PPSECh. 3.5 - Prob. 11PPSECh. 3.5 - Prob. 12PPSECh. 3.5 - Prob. 13PPSECh. 3.5 - Prob. 14PPSECh. 3.5 - Prob. 15PPSECh. 3.5 - Prob. 16PPSECh. 3.5 - Prob. 17PPSECh. 3.5 - Prob. 18PPSECh. 3.5 - Prob. 19PPSECh. 3.5 - Prob. 20PPSECh. 3.5 - Prob. 21PPSECh. 3.5 - Prob. 22PPSECh. 3.5 - Prob. 23PPSECh. 3.5 - Prob. 24PPSECh. 3.5 - Prob. 25PPSECh. 3.5 - Prob. 26PPSECh. 3.5 - Prob. 27PPSECh. 3.5 - Prob. 28PPSECh. 3.5 - Prob. 29PPSECh. 3.5 - Prob. 30PPSECh. 3.5 - Prob. 31PPSECh. 3.5 - Prob. 32PPSECh. 3.5 - Prob. 33PPSECh. 3.5 - Prob. 34PPSECh. 3.5 - Prob. 35PPSECh. 3.5 - Prob. 36PPSECh. 3.5 - Prob. 37PPSECh. 3.5 - Prob. 38PPSECh. 3.5 - Prob. 39PPSECh. 3.5 - Prob. 40PPSECh. 3.5 - Prob. 41PPSECh. 3.5 - Prob. 42PPSECh. 3.5 - Prob. 43PPSECh. 3.5 - Prob. 44PPSECh. 3.5 - Prob. 45PPSECh. 3.6 - Prob. 1LCCh. 3.6 - Prob. 2LCCh. 3.6 - Prob. 3LCCh. 3.6 - Prob. 4LCCh. 3.6 - Prob. 5LCCh. 3.6 - Prob. 6LCCh. 3.6 - Prob. 7LCCh. 3.6 - Prob. 8PPSECh. 3.6 - Prob. 9PPSECh. 3.6 - Prob. 10PPSECh. 3.6 - Prob. 11PPSECh. 3.6 - Prob. 12PPSECh. 3.6 - Prob. 13PPSECh. 3.6 - Prob. 14PPSECh. 3.6 - Prob. 15PPSECh. 3.6 - Prob. 16PPSECh. 3.6 - Prob. 17PPSECh. 3.6 - Prob. 18PPSECh. 3.6 - Prob. 19PPSECh. 3.6 - Prob. 20PPSECh. 3.6 - Prob. 21PPSECh. 3.6 - Prob. 22PPSECh. 3.6 - Prob. 23PPSECh. 3.6 - Prob. 24PPSECh. 3.6 - Prob. 25PPSECh. 3.6 - Prob. 26PPSECh. 3.6 - Prob. 27PPSECh. 3.6 - Prob. 28PPSECh. 3.6 - Prob. 29PPSECh. 3.6 - Prob. 30PPSECh. 3.6 - Prob. 31PPSECh. 3.6 - Prob. 32PPSECh. 3.6 - Prob. 33PPSECh. 3.6 - Prob. 34PPSECh. 3.6 - Prob. 35PPSECh. 3.6 - Prob. 36PPSECh. 3.6 - Prob. 37PPSECh. 3.6 - Prob. 38PPSECh. 3.6 - Prob. 39PPSECh. 3.6 - Prob. 40PPSECh. 3.6 - Prob. 41PPSECh. 3.6 - Prob. 42PPSECh. 3.6 - Prob. 43PPSECh. 3.6 - Prob. 44PPSECh. 3.6 - Prob. 45PPSECh. 3.6 - Prob. 46PPSECh. 3.6 - Prob. 47PPSECh. 3.6 - Prob. 48PPSECh. 3.6 - Prob. 49PPSECh. 3.6 - Prob. 50PPSECh. 3.6 - Prob. 51PPSECh. 3.6 - Prob. 52PPSECh. 3.6 - Prob. 53PPSECh. 3.6 - Prob. 54PPSECh. 3.6 - Prob. 55PPSECh. 3.6 - Prob. 56PPSECh. 3.6 - Prob. 57PPSECh. 3.6 - Prob. 58PPSECh. 3 - Prob. 1GRCh. 3 - Prob. 2GRCh. 3 - Prob. 3GRCh. 3 - Prob. 4GRCh. 3 - Prob. 5GRCh. 3 - Prob. 6GRCh. 3 - Prob. 7GRCh. 3 - Prob. 8GRCh. 3 - Prob. 9GRCh. 3 - Prob. 10GRCh. 3 - Prob. 11GRCh. 3 - Prob. 12GRCh. 3 - Prob. 13GRCh. 3 - Prob. 14GRCh. 3 - Prob. 15GRCh. 3 - Prob. 16GRCh. 3 - Prob. 17GRCh. 3 - Prob. 18GRCh. 3 - Prob. 19GRCh. 3 - Prob. 20GRCh. 3 - Prob. 21GRCh. 3 - Prob. 22GRCh. 3 - Prob. 23GRCh. 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. 1CVCh. 3 - Prob. 2CVCh. 3 - Prob. 3ECh. 3 - Prob. 4ECh. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - Prob. 7ECh. 3 - Prob. 8ECh. 3 - Prob. 9ECh. 3 - Prob. 10ECh. 3 - Prob. 11ECh. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Prob. 16ECh. 3 - Prob. 17ECh. 3 - Prob. 18ECh. 3 - Prob. 19ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Prob. 23ECh. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 30ECh. 3 - Prob. 1CTCh. 3 - Prob. 2CTCh. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - Prob. 1CCSRCh. 3 - Prob. 2CCSRCh. 3 - Prob. 3CCSRCh. 3 - Prob. 4CCSRCh. 3 - Prob. 5CCSRCh. 3 - Prob. 6CCSRCh. 3 - Prob. 7CCSRCh. 3 - Prob. 8CCSRCh. 3 - Prob. 9CCSRCh. 3 - Prob. 10CCSRCh. 3 - Prob. 11CCSRCh. 3 - Prob. 12CCSRCh. 3 - Prob. 13CCSRCh. 3 - Prob. 14CCSRCh. 3 - Prob. 15CCSRCh. 3 - Prob. 16CCSRCh. 3 - Prob. 17CCSRCh. 3 - Prob. 18CCSRCh. 3 - Prob. 19CCSRCh. 3 - Prob. 20CCSRCh. 3 - Prob. 21CCSRCh. 3 - Prob. 22CCSRCh. 3 - Prob. 23CCSR
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