Chapter 3 Linear Systems and Matrices - 3.4 Solve Systems of Linear Equations in Three Variables - 3.4 Exercises - Skill Practice - Page 182: 16

$x=5$ $y=0$ $z=-5$

Given: $2x-y-z=15$ $\rightarrow z=2x-y-15$ Substitute for z in the second equation: $4x + 5y + 2z = 10$ $4x+5y+2(2x-y-15)=10$ $4x+5y+4x-2y-30=10$ $8x+7y=40$ (1) Substitute for z in the third equation: $-x -4y + 3z = -20$ $-x-4y+3(2x-y-15)=-20$ $5x-7y=25$ (2) From (1) and (2): $8x+7y=40$ $5x-7y=25$ ________________ $13x=65$ $x=5$ Solve for y: $8.5+7y=40$ $y=0$ Solve for z: $z=2.5-0-15=-5$