Chapter 3 Linear Systems and Matrices - 3.5 Perform Basic Matrix Operations - 3.5 Exercises - Quiz for Lessons 3.3-3.5 - Page 193: 8

$x=4$ $y=-2$ $z=-5$

Use elimination for the equations: $x +y + z =-3$ $2x - 3y + z= 9$ Multiply both sides of the first equation by $-1$ $-x -y - z =3$ $2x - 3y + z= 9$ ________________________ $x-4y=12$ (1) $x +y + z =-3$ $4x - 5y + 2z = 16$ Multiply the first equation by $-2$: $-2x -2y -2 z =6$ $4x - 5y + 2z = 16$ ____________________ $2x-7y=22$ (2) From (1) and (2): $x-4y=12$ $2x-7y=22$ Multiply both sides of the first equation by $-2$ $-2x+8y=-24$ $2x-7y=22$ ___________________ $y=-2$ Solve for x: $x-4(-2)=12$ $x=4$ Solve for z: $4+(-2)+z=-3$ $z=-5$