Question 475310
I think the best way to do these is using the elimination method.
Eliminate a variable to break it down into a system of 2 equations, then use elimination again to break it down to a single equation. Solve for that variable and then use substitution to find the 2nd variable in the system of 2 equations. Then substitute both those values into one of the original equations to find 3rd variable. 
Let me label each equation: A,B,C for reference
A:{{{2x + 4y + 4z = 16}}}
B:{{{2x - y + 3z = 9}}}
C:{{{3x + 4y - z = 8}}}
Notice A and C both have a 4y, therefore it will be easiest to eliminate variable y. Multiply C by -1. Add A and C. Call the resulting equation D.
D:{{{-x + 5z = 8}}}
We still need another equation with x and z. To eliminate y again. Multiply B by 4. Add A and B. Call the resulting equation E.
E:{{{10x + 16z = 52}}}
Now eliminate x. Multiply D by 10. Add D and E.
{{{66z = 132}}}
Solve for z. Divide by 66 on both sides.
{{{z = 2}}}
Substitute z=2 into D.
{{{-x + 5(2) = 8}}}
Solve for x. 
{{{-x + 10 = 8}}}
Subtract 10 on both sides
{{{-x = -2}}}
Flip signs
{{{x = 2}}}
Substitute x=2, z=2 into B.
{{{2(2) - y + 3(2) = 9}}}
Solve for y
{{{4 - y + 6 = 9}}}
{{{-y + 10 = 9}}}
Subtract 10 on both sides
{{{-y = -1}}}
Flip signs
{{{y = 1}}}
Verify solution by substituting into other equations A and C.
{{{2(2) + 4(1) + 4(2) = 16}}}
{{{4+4+8 = 16}}}
{{{16 = 16}}}
True...it works.
{{{3(2) + 4(1) - 2 = 8}}}
{{{6 + 4 - 2= 8}}}
{{{8=8}}}
True..it works.
Solution is x = 2, y = 1, z = 2