Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 3.5, Problem 6CYU
To determine

To calculate: The solution set of system of equations,

  2a−3b+5c=58−5a+b−4c=−51−6a−8b+c=22

Expert Solution & Answer
Check Mark

Answer to Problem 6CYU

The solution set of the system of equations is (3,−4,8).

Explanation of Solution

Given information:

The system of equations is provided below,

  2a−3b+5c=58−5a+b−4c=−51−6a−8b+c=22

Formula used:

A system of equations with three variables can be solved by elimination method and substitution method. Select any two pairs of equations from the system and eliminate the same variable by adding or subtracting and then simplify it.

Calculation:

Consider the provided system of equations as,

  2a−3b+5c=58−5a+b−4c=−51−6a−8b+c=22

Recall that a system of equations with three variables can be solved by elimination method and substitution method. Select any two pairs of equations from the system and eliminate the same variable by adding or subtracting and then simplify it.

So, multiply the second equation by 8 and then add third and the resulting equation to eliminate b .

  8(−5a+b−4c)=8(−51)−40a+8b−32c=−408

Now add the third and the resulting equation as,

  −40a+8b−32c=−408(+)−6a−8b+c=22−46a−31c=−386

Now, multiply second equation by 3 and add first equation and second equation to eliminate b .

  3(−5a+b−4c)=3(−51)−15a+3b−12c=−153

Add this equation and first equation as,

  2a−3b+5c=58(+)−15a+3b−12c=−153−13a−7c=−95

Multiply −46a−31c=−386 by −7 and multiply −13a−7c=−95 by 31 and then add both the equations to eliminate c as,

  −7(−46a−31c)=−7(−386)322a+217c=2702

  31(−13a−7c)=31(−95)−403a−217c=−2945

Add both the equations and solve to find the value of a ,

  322a+217c=2702(+)−403a−217c=−2945−81a=−243

Simplify −81a=−243 as,

  −81a=−243a=−243−81a=3

Substitute a=3 in −46a−31c=−386 to get the value of c ,

  −46(3)−31c=−386−138−31c=−386−31c=−248c=8

Now, substitute a=3 and c=8 in equation second to get the value of b as,

  −5(3)+b−4(8)=−51−15+b−32=−51b−47=−51b=−4

To check whether the solution set is correct, substitute the values of a , b and c in first equation as,

  2a−3b+5c=582(3)−3(−4)+5(8)=586+12+40=5858=58

Since, left-hand side is equal to right-hand side, the solution set is true for all the equations.

Thus, the solution set of the system of equations is (3,−4,8).

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Chapter 3.5, Problem 5CYU
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Chapter 3.5, Problem 7CYU

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
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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 - 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