How do I write systems of equations in matrix form?

That's one of the easiest things you'll ever learn:

Suppose you have this system:

4x + 7y =  1
 x -  y = -8

Look at the red numbers:

4x + 7y =  1
1x - 1y = -8

Erase the letters:

4  + 7  =  1
1  - 1  = -8


Erase the + and bring the - over nearer the 1:

4    7  =  1
1   -1  = -8

Replace the " = " signs with a vertical bar:

4    7  |  1
1   -1  | -8

Put a bracket around the whole thing.  Some
books and teachers use brackets and others use 
parentheses.

[4   7  |  1]
[1  -1  | -8]

If you have:

5z = 38 + 3y - 2x
2y + 38 = 8z - 4x
3x + 2z = 4y + 28 

you must first arrange them so that the
letters line up vertically, like this:

2x - 3y + 5z =  38
4x + 2y - 8z = -38
3x - 4y + 2z =  28

Then it's easy to form the matrix:

[2  -3   5 |  38]
[4   2  -8 | -38]
[3  -4   2 |  28]

Edwin