Chapter 3 Linear Systems and Matrices - 3.5 Perform Basic Matrix Operations - 3.5 Exercises - Quiz for Lessons 3.3-3.5 - Page 193: 7

$z=1$ $y=-4$ $x=2$

Use elimination for the equations: $x + 2y - 5z =-11$ $-x - 3y = 10$ ________________________ $-y-5z=-1$ (1) $2x - y - 3z = 5$ $-x - 3y = 10$ Multiply the second equation by $2$: $2x - y - 3z = 5$ $-2x - 6y = 20$ ____________________ $-7y-3z=25$ (2) From (1) and (2): $-y-5z=-1$ $-7y-3z=25$ Multiply both sides of the first equation by $-7$: $7y+35z=7$ $-7y-3z=25$ ___________________ $32z=32$ $z=1$ Solve for y: $-y-5(1)=-1$ $y=-4$ Solve for x: $x+2(-4)-5(1)=-11$ $x=2$