we should eliminate one vairable from all equations so we get 2, 2 variable equations
eliminate x
add 1st and 2nd equations
x-3y+2z=1
-x+4y-4z=1 +
0x+y-2z=2
y-2z=2, this is equation A
now, eliminate x from last equation
multily 2nd equation by 5 and add to 2nd
-5x+20y-20z=5
5x-y+6z=9 +
0x+19y-14z=14
equationB is 19y-14z=14
now we have
y-2z=2
19y-14z=14
we cann solve for y in first equation and sub for y
y=2+2z
sub that for y
19(2+2z)-14z=14
38+38z-14z=14
38+24z=14
minus 38 both sides
24z=-24
divide both sides by 24
z=-1
sub back
y=2+2z
y=2+2(-1)
y=2-2
y=0
now sub back into first equation
x-3(0)+2(-1)=1
x-0-2=1
x-2=1
add 2
x=3
x=3
y=0
z=-1
(x,y,z)
(3,0,-1)
tada
