Chapter 3 - Section 3.3 - Systems of Linear Equations in Three Variables - Exercise Set - Page 215: 12

$(1,1,2)$

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