How to solve system of equations?

Question

Can someone solve this for me :( 
I know the steps but with this equation I'm stuck... 

w + x + y + z = 0 
2w + 2x - 2y - 2z = 16 
3w - 2x + 2y + z = 2 
w - x + 3y + 3z = -10

Answer 1

The equations are w + x + y + z = 0 ---> (1)

2w  + 2x  - 2y  - 2z  = 16 ---> (2)

3w  - 2x  + 2y  + z  = 2 ---> (3)

w - x + 3y  + 3z  = - 10 ---> (4)

2*(1) ⇒ 2w  + 2x  + 2y  + 2z  = 0 ---> (5)

To eliminate x  variable add the equations (1) & (4).

(w  + x  + y  + z  = 0) + (w  - x  + 3y  + 3z  = - 10) ⇒ 2w  + 4y  + 4z  = - 10 ---> (6)

To eliminate x  variable add the equations (5)&(3).

(2w  + 2x  + 2y  + 2z  = 0) + (3w  - 2x  + 2y  + z  = 2) ⇒ 5w  + 4y  + 3z  = 2 ---> (7)

To eliminate y  variable subtract the equations (7) from (6).

(2w + 4y  + 4z  = -10) - (5w + 4y  + 3z  = 2) ⇒ -3w  + z  = -12 ---> (8)

To eliminate y, z  variable add the equations (5) & (3).

(2w  + 2x + 2y  + 2z  = 0) + (3w  - 2x  + 2y  + z  = 2) ⇒ 5w - z  = 18 ---> (9)

To eliminate z  variable add the equations (8) & (9).

(- 3w  + z  = - 12) + (5w  - z  = 18) ⇒ 2w  = 6 ⇒ w = 3

Substitute the w  value in 5w  - z  = 18 .

15 - z  = 18 ⇒ z  = -3

Substitute the w , z  values in 5w  + 4y  + 3z  = 2.

15 + 4y  - 9 = 2

4y  = -4 ⇒ y  = - 1

Substitute the w , z  ,y   values in w  + x  + y  + z  = 0.

3 + x  - 1 - 3 = 0

x  = 1

Solution x = 1 , y = - 1 , z  = -3, w = 3 .