Chapter 3 - Section 3.3 - Systems of Linear Equations in Three Variables - Exercise Set - Page 215: 8

$(1,-1,2)$

To solve the given problem we will have to plug the simplest equation into the other equation and then solve for the other variable. $x-y+3z=8$ and $3x+y-2z=-2$ This gives, $4x+z=6$ Now, $20x+5z=30$ and $-20x+18z=16$ This gives $z=2$ Now, $4x+2=6$ or, $x=1$ Also, $x-y+3z=8$ $-y+7=81$ or, $y=-1$ Hence, the desired result is $(1,-1,2)$