Chapter 10 - Section 10.2 - Systems of Linear Equations in Several Variables - 10.2 Exercises - Page 697: 18

$x=1$ $y=0$ $z=-1$

Express y from the second equation. $x-y+z=0$ $y+2z=-2\rightarrow y=-2-2z$ $x+y-z=2$ Substitute $ y=-2-2z$ into the first and the third equation. $x-(-2-2z)+z=0$ $x+(-2-2z)-z=2$ Simplify. $x+3z=-2$ $x-3z=4$ Add the equations to eliminate z. $2x=2$ $x=1$ Substitute for x and solve for y and z. $x+3z=-2 \rightarrow z=-1$ $y=-2-2z \rightarrow y=0$