Chapter 3 - Section 3.3 - Systems of Linear Equations in Three Variables - Exercise Set - Page 215: 13

$(1,0,-3)$

Use the addition method for the first two equations. $-2x-y=-2$ $x+y-z=4$ $-x-z=2$ Use the addition method for the last two equations. $-2x-2y+2z=-8$ $3x+2y+z=0$ $x+3z=-8$ Solve for x and z with the two variable equations. $-x-z=2$ $x+3z=-8$ $2z=-6$ $z=-3$ $-x-(-3)=2$ $-x+3=2$ $-x=-1$ $x=1$ To find y, substitute values for x. $-2(1)-y=-2$ $-y=0$ $y=0$