Chapter 3 Linear Systems and Matrices - 3.4 Solve Systems of Linear Equations in Three Variables - 3.4 Exercises - Skill Practice - Page 182: 19

$x=0$ $y=0$ $z=-2$

The first equation: $2x-y+z=-2$ Solve for z: $z=-2x+y-2$ Substitute for z in the second equation: $6x+3y−4z=8$ $6x+3y−4(-2x+y-2)=8$ $6x+3y+8x-4y+8=8$ $14x-y=0$ $y=14x$ Substitute for z in the third equation: $−3x+2y+3z=−6$ $−3x+2y+3(-2x+y-2)=−6$ $-3x+2y-6x+3y-6=-6$ $-9x+5y=0$ (*) Substitute for y: $-9x+5(14x)=0$ $61x=0$ $x=0$ Solve for y: $y=14(0)=0$ Solve for z: $z=-2.0+0-2=-2$