## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 3 Linear Systems and Matrices - Cumulative Review Chapters 1-3 - Page 232: 33

#### Answer

The solution is $(-2,4,1)$

#### Work Step by Step

Use elimination for the first two equations: $x - y + 2z = -4$ $3x + y - 4z=-6$ ______________________ $4x-2z=-10$ (1) Add $-3$ times equation 2 to equation 3: $-9x -3y +12z =18$ $2x + 3y + z = 9$ __________________________ $-7x+13z=27$ (2) Add 7 times equation (1) to $4$ times equation (2): $28x-14z=-70$ $-28x+52z=108$ ____________________ $38z=38$ $z=1$ Solve for x: $4x-2(1)=-10$ $x=-2$ Solve for y: $-2-y+2(1)=-4$ $y=4$ The solution is $(-2,4,1)$.

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