Line up like letters
Line up the equal sign
Line up the numbers on the right sides:

z - d -  b = 200
z     + 2b = 250
         b = 150

Put 1 coefficients which are usually left understood:

1z - 1d -  1b = 200
1z      +  2b = 250
           1b = 150

Put in place holder "+ 0 times the letter" terms for 
the missing letters in the second and third 
equations:

1z - 1d - 1b = 200
1z + 0d + 2b = 250
0z + 0d + 1b = 150

That can be abbreviated by a matrix by erasing
all the letters and putting the - signs close to the 
numbers, and erasing the + signs. Erase the = signs.

[1   -1   -1   200]
[1    0    2   250]
[0    0    1   150]

Press 2ND MATRIX (the x-1 key).
Highlight EDIT.
Press ENTER.

Make it read  MATRIX[A] 3 x 4

type in all the numbers in the above matrix. The
brackets "[" and "]" are already there.

Press 2ND QUIT (the MODE key)
Press CLEAR

Press 2ND MATRIX (the x-1 key).

Highlight MATH
Scroll with arrow to B:rref(
Press ENTER

See rref( followed by blinking cursor.

Press 2ND MATRIX (the x-1 key)

Press ENTER

See rref([A]

Press ) then ENTER

Screen should read

rref([A])
  [[1 0 0 -50 ]
   [0 1 0 -400] 
   [0 0 1 150 ]]

This means

1x + 0y + 0z = -50
0x + 1y + 0z = -400
0x + 0y + 1z = 150

or erasing the placeholder terms and the 1
coefficients:

 x           = -50
      y      = -400
           z = 150

Edwin