SOLUTION: Solve each system {{{system( (x+2)/6 - (y+4)/3 + z/2 = 0, (x+1)/2 + (y-1)/2 - z/4 = 9/2, (x-5)/4 + y+1 + (z-2)/2 = 19/4)}}}

 

We clear each of fractions:

Clearing the first of fractions by multiplying
through by LCD of 6

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

and simplifying:

x + 2 - 2y - 4 + z = 0
x - 2y + z - 2 = 0
x - 2y + z = 2

Clearing the second of fractions by multiplying
through by LCD of 4
2(x+1) + 2(y-1) - z = 18,

and simplifying:

2x + 2 + 2y - 2 - z = 18
2x + 2y - z = 18

Clearing the third equation of fractions 
by multiplying through by LCD of 4
(x-5) + 4(y+1) + 2(z-2) = 19

and simplifying:

x - 5 + 4y + 4 + 2z - 4 = 19
x + 4y + 2z - 5 = 19
x + 4y + 2z = 24

Now the system is simple enough for you to solve:

 

Solve that and get (x,y,z) = (,,2)

Edwin