System of Equations

your solution for $(x, y, z)$ is $(-3, 1, 0).$ if you would like steps, please tell. otherwise, hope this helped. 

6x + 8y - 3z = -10     (1)

2x + 8y - 5z = 2        (2)

-5x - 8y + 4z = 7       (3)

Add ( 1)  and (3)   and we have

x + z =   -3       (4)

Add ( 2)  and (3)  and we have

-3x - z  =  9         (5)

Add ( 4)  and (5) and we  have  that

-2x  =  6

x =  6 /  -2  =  -3

And

x + z  = -3

-3 + z  =  -3

z  = 0

And

6(-3)  + 8y  - 3(0) = -10

-18   + 8y  = -10

8y  = 8

y  = 1

So  ( x,  y , z)  =   ( -3 , 1 , 0)  as CentsLord  found