   # For problems 114-118, solve each of the systems of equations. ( 4 x − y + 3 z = − 12 2 x + 3 y − z = 8 6 x + y + 2 z = − 8 ) ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 10.CM, Problem 117CM
Textbook Problem
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## For problems 114-118, solve each of the systems of equations. ( 4 x − y + 3 z = − 12 2 x + 3 y − z = 8 6 x + y + 2 z = − 8 )

To determine

To solve:

The systems of equation (4xy+3z=122x+3yz=86x+y+2z=8).

### Explanation of Solution

Calculation:

To solve the equation (4xy+3z=122x+3yz=86x+y+2z=8).

To rewrite the equation,

4xy+3z=12...(1)2x+3yz=8...(2)6x+y+2z=8...(3)

From (1) 4xy+3z=12 subtract y+3z from both sides,

4xy+3z(y+3z)=12(y+3z)

4x=12+y3z

Divide both sides by 4,

4x4=124+y43z4

x=12+y3z4

Substitute x=12+y3z4 in equation (2) and (3).

212+y3z4+3yz=8...(3)612+y3z4+y+2z=8...(4)

Add z to both sides in equation (3)

212+y3z4+3yz+z=8+z212+y3z4+3y=8+z...(5)

Expand the term, 212+y3z4+3y

=y3z122+3y

=12+y3z2+3y22=12+y3z+3y22

=7y3z122

=7y23z2