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 3CYU
To determine

To calculate: The solution set of system of equations,

  3x+6y−2z=−62x+y+4z=19−5x−2y+8z=62

Expert Solution & Answer
Check Mark

Answer to Problem 3CYU

The solution set of the system of equations is (−4,3,6).

Explanation of Solution

Given information:

The system of equations is provided below,

  3x+6y−2z=−62x+y+4z=19−5x−2y+8z=62

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,

  3x+6y−2z=−62x+y+4z=19−5x−2y+8z=62

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 2 and then add second and the third equation to eliminate y .

  2(2x+y+4z)=2(19)4x+2y+8z=38

Now add the second and the third equation as,

  4x+2y+8z=38(+)−5x−2y+8z=62−x+16z=100

Now, multiply second equation by −6 and add first equation and second equation to eliminate y .

  −6(2x+y+4z)=−6(19)−12x−6y−24z=−114

Add second equation and the first equation as,

  3x+6y−2z=−6(+)−12x−6y−24z=−114−9x−26z=−120

Multiply −x+16z=100 by −9 and add resulting equation and −9x−26z=−120 to eliminate x as,

  −9(−x+16z)=−9(100)9x−144z=−900

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

  −9x−26z=−120(+)9x−144z=−900−170z=−1020

Simplify −170z=−1020 as,

  −170z=−1020z=−1020−170z=6

Substitute z=6 in −x+16z=100 to get the value of x ,

  −x+16(6)=100−x+96=100−x=4x=−4

Now, substitute x=−4 and z=6 in equation second to get the value of y as,

  2(−4)+y+4(6)=19−8+y+24=19y+16=19y=3

To check whether the solution set is correct, substitute the values of x , y and z in first equation as,

  3x+6y−2z=−63(−4)+6(3)−2(6)=−6−12+18−12=−6−6=−6

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 (−4,3,6).

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Chapter 3.5, Problem 2CYU
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Chapter 3.5, Problem 4CYU

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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