X-3y+2=1
-x+4y-4z=1
5x- y +6z =9
write your answer in the form (x, y, z)

!

X = 3y - 1
y=4y−4z−1
z= 1/5‌y+ ‌−6/5‌z+‌9/5

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