Let -x - 5y - 5z = 2 be ( Eq. 1 ), 4x - 5y + 4z = 19 be ( Eq. 2 ) and x + 5y - z = -20 be ( Eq. 3 ).
Add ( Eq. 1 ) and ( Eq. 2 ) to eliminate x and y, that is:
- 6z = - 18
z = 3
Substract ( Eq. 1 ) and ( Eq. 2 ) to get ( 4 ) and to eliminate y, and that is:
- 5x - 9z = - 17 ( 4 )
Substitute the value of z to ( Eq. 4 ), that is:
- 5x - 9 ( 3 ) = - 17
- 5x = 10
x = - 2
Substitute the value of x and z to ( Eq. 1 ) to get the value of y, and that is:
4 ( - 2 ) - 5y + 4 ( 3 ) = 19
- 8 - 5y + 12 = 19
- 5y = 15
y = - 3
Thus, the value of x, y, and z is 2, - 3, and 3, respectively.