Solve by elimination

-4x-5y-z=18

-2x-5y-2z=12

-2x+5y+2z=4

So

-4x-5y-z=18

-2x-5y-2z=12

-2x+5y+2z=4

the 2 last equations look perfect for canceling each other so add them together

-2x-5y-2z=12

-2x+5y+2z=4 +

-4x+0y+0z=16

-4x=16

divide both sides by 4

-x=4

multiply - 1

x=-4

now we have

-4x-5y-z=18

-2x+5y+2z=4

add them together

-6x+0y+z=22

but x=-4 so

-6 (-4) + z=22

24+z=22

subtract 24 from both sides

z = - 2

subsitute into any equation

-2x-5y-2z=12

x=-4

z=-2

-2 (-4) - 5y-2 (-2) = 12

8-5y+4=12

12-5y=12

subtract 12 from both sides

-5y=0

y=0

x=-4

y=0

z=-2

-4x - 5y - 1z = 18 ⇒ - 4x - 5y - 1z = 18

-2x - 5y - 2z = 12 ⇒ - 2x - 5y - 2z = 12

-2x + 5y + 2z = 4 - 6x - 10y - 3z = 30

-6 (-4) - 10y - 3z = 30

-4x - 5y - 1z = 18 24 - 10y - 3z = 30

-2x - 5y - 2z = 12 ⇒ - 2x - 5y - 2z = 12 - 24 - 24

-2x + 5y + 2z = 4 ⇒ - 2x + 5y + 2z = 4 - 10y - 3z = 6

-4x = 16 - 10y + 10y - 3z = 6 + 10y

-4 - 4 - 3z = 6 + 10y

x = - 4 - 3 - 3

z = - 2 - 3¹/₃y

-10y - 3 (-2 - 3¹/₃y) = 6

-10y + 6 + 10y = 6

-10y + 10y + 6 = 6

0y + 6 = 6

- 6 - 6

0y = 0

0 0

y = 0

-10 (0) - 3z = 6

-0 - 3z = 6

0 - 3z = 6

- 0 - 0

-3z = 6

-3 - 3

z = - 2

(x, y, z) = (-4, 0, - 2)