(1) 4w+x+2y-3z=-16
(2) -3w+3x-y+2z=20
(3) 5w+4x+3y-z=-10
(4) -w+2x+5y+z=-4
(5)=(3)+(4)=4w+6x+8y=-14⇒2w+3x+4y=-7 (5)
(6)=(2)+2(3)=7w+11x+5y=0 (6)
(7)=(1)+3(4)=w+7x+17y=-28, w=-28-7x-17y (7)
Substitute for w in (5) and (6):
(8) -56-14x-34y+3x+4y=-7, -11x-30y=49, 11x+30y=-49 (8)
(9) -196-49x-119y+11x+5y=0, -38x-114y=196, 38x+114y=-196, 19x+57y=-98 (9)
(10)=57(8)-30(9)=627x+1710y-570x-1710y=-2793+2940, 57x=147, x=147/57=49/19.
Therefore y=(-49-11x)/30=-49/19; w=-28-7x-17y=-42/19; z=5w+4x+3y+10=29/19.