Help solving this equation using matrices...

Can anybody help me solve this?
I need to find what numbers go into x, y, and z that satisfies equation.

4x - 5y + 3z = 1
2x - 3y - 5z = 39
x - 2y = 4

Set up augmented matrix:

[ 4 .. -5 ... 3 .... 1 ]
[ 2 .. -3 .. -5 .. 39 ]
[ 1 .. -2 ... 0 .... 4 ]

Switch rows (but never columns) to make solving easier, i.e. put row that starts with 1 at top

[ 1 .. -2 ... 0 .... 4 ]
[ 4 .. -5 ... 3 .... 1 ]
[ 2 .. -3 .. -5 .. 39 ]

Perform elementary row operations to reduce 3x3 matrix on left to identity matrix:
R2 = R2 - 4*R1 = [4 -5 3 1] - [4 -8 0 16] = [0 3 3 -15]
R2 = R2/3 = [0 1 1 -5]
R3 = R2 - 2*R1 = [2 -3 -5 39] - [2 -4 0 8] = [0 1 -5 31]

[ 1 .. -2 ... 0 .... 4 ]
[ 0 ... 1 ... 1 ... -5 ]
[ 0 ... 1 .. -5 .. 31 ]

R1 = R1 + 2*R2 = [1 -2 0 4] + [0 2 2 -10] = [1 0 2 -6]
R3 = R2 - R3 = [0 1 1 -5] - [0 1 -5 31] = [0 0 6 -36]
R3 = R3/6 = [0 0 1 -6]

[ 1 ... 0 ... 2 ... -6 ]
[ 0 ... 1 ... 1 ... -5 ]
[ 0 ... 0 ... 1 ... -6 ]

R1 = R1 - 2*R3 = [1 0 2 -6] - [0 0 2 -12] = [1 0 0 6]
R2 = R2 - R3 = [0 1 1 -5] - [0 0 1 -6] = [0 1 0 1]

[ 1 ... 0 ... 0 .... 6 ]
[ 0 ... 1 ... 0 .... 1 ]
[ 0 ... 0 ... 1 ... -6 ]

x = 6
y = 1
z = -6

Mαthmφm

It would be so long to explain, watch this video
http://www.youtube.com/watch?v=hu6B1d3vv…
Inverse matrices

I don't know if you are solving by reduced echelon or inverse, this video is on inverses, there is also one on echelon