Chapter 3 Linear Systems and Matrices - 3.4 Solve Systems of Linear Equations in Three Variables - 3.4 Exercises - Skill Practice - Page 182: 15

$x=3$ $y=2$ $z=1$

Given: $x+y-z=4$ $\rightarrow x=-y+z+4$ Substitute for x in the second equation: $3x + 2y + 4z = 17$ $3(-y+z+4)+2y+4z=17$ $-3y+3z+12+2y+4z=17$ $-y+7z=5$ (1) Substitute for x in the third equation: $-x + 5y + z = 8$ $-(-y+z+4)+5y+z=8$ $y-z-4+5y+z=8$ $6y=12$ $y=2$ Substitute for y in the first equation: $-2+7z=5$ $7z=7$ $z=1$ Solve for x: $x=-2+1+4=3$