help with system

Solve the system of equations

10b+5v+5z=55  
3b+5v+5z=34
5b+6v+3z=42

10b+5v+5z=55               5z=55-10b-5v
3b+5v+5z=34                 5z=34-3b-5v

55-10b-5v=34-3b-5v   | + 5v                    system of equations        

55-10b=34-3b             | -34+10b

21=7b                          | /7

b=3

3b+5v+5z=34              |deploy b=3         system of deploy
5b+6v+3z=42              |deploy b=3

9+5v+5z=34                | * 3 
15+6v+3z=42              | * 5

27+15v+15z=170        | subtr.                 system of addition

75+30v+15z=210

48+15v=40                  | -48

15v=-8                         | /15

v=$-\frac{8}{15}$

27+15v+15z=170        | deploy $v=-\frac{8}{15}$   

27-8+15z=170            | - 19

15z=151

$z=10\frac{1}{15}$

  !