Given equations: 2x+2y+z = -5 -----------(1) 3x+4y+2z = 0 ----------(2) x+3y+2z = 1 ---------(3) Subtract equation (3) from equation (2) to eliminate z 3x+4y+2z =0 -x-3y-2z=-1 __________ 2x+y=-1 -------------------(4) Multiply equation (1) by 2 and subtract it from equation (3) to eliminate z x+3y+2z=1 -4x-4y-2z=10 ____________ -3x-y=11 --------(5) Add equation (4) and (5) to eliminate y 2x+y=-1 -3x-y=11 _______ -x=10 X=-10 Substitute the value of x in equation (4) to find y 2(-10)+y=-1 -20+y=-1 y=-1+20 y=19 Substitute the values of x and y in any one of the 3 equations, to find z. Let’s substitute in equation (1) 2(-10)+2(19)+z=-5 -20+38+z=-5 18+z=-5 z=-5-18 z=-23 Therefore the solution is: x=-10, y=19, z=-23
