LINEAR4 hp32sII
A program to solve a linear system of 4 equations with 4 unknowns. 

System:

  Ax+By+Cz+Dw = E   (A NOT ZERO)
  Fx+Gy+Hz+Iw = J
  Kx+Ly+Mz+Nw = O
  Px+Qy+Rz+Sw = T

The program stores all coefficients in the memory of the same
letter variable. The input is by row including the independent terms:
A,B,C,D,E, F,G,H,.... There is a small pause before input the last
row (P,Q,R,S,T) due to the need to do some calculations to empty four
variables (i,G,M,N) because of the memory limitations of the hp32sII.
The results for x,y,z,w are shown in the corresponding stack registers
(use roll to see them).

WARNINGS:
The program clears ALL variables (not sums) before starting.
To save memory, the program is very primitive; it does not do pivoting,
and it may fail in some few instances even for non singular
matrices (change the order of the rows if this happens or if A is zero).
You can also use this program to solve systems with only 3 or 2 
unknowns. For example, to solve a 2x2 system (x,y unknowns) enter the 
equivalent 4x4 system:

  Ax+By+0z+0w = E   (A NOT ZERO)
  Fx+Gy+0z+0w = J
  0x+0y+1z+0w = 0
  0x+0y+0z+1w = 0

Memory requirements:
  Total:340.5 bytes. Program:204.5 bytes. Variables:136 bytes (8x17).
  Left free: 43.5 bytes. No Flags used.
  B CHKSUM=56F9   23.0
  L CHKSUM=8112  181.5

x--------------x--------------x--------------x--------------x-----------
B01 LBL B      L01 LBL L      L11 RCL C      L21 RCLx K     L31 STO- O
B02 CLVARS     L02 INPUT(i)   L12 RCLx F     L22 STO- L     L32 RCL G
B03 7.015      L03 RCL A      L13 STO- H     L23 RCL C      L33 STOx M
B04 STO i      L04 STOx (i)   L14 RCL D      L24 RCLx K     L34 STOx N
B05 INPUT A    L05 ISG i      L15 RCLx F     L25 STO- M     L35 STOx O
B06 INPUT B    L06 GTO L      L16 STO- I     L26 RCL D      L36 RCL H
B07 INPUT C    L07 STO/ K     L17 RCL E      L27 RCLx K     L37 RCLx L
B08 INPUT D    L08 RCL B      L18 RCLx F     L28 STO- N     L38 STO- M
B09 INPUT E    L09 RCLx F     L19 STO- J     L29 RCL E      L39 RCL I
B10 INPUT F    L10 STO- G     L20 RCL B      L30 RCLx K     L40 RCLx L

L41 STO- N     L51 INPUT Q    L61 RCL B      L71 RCLx P     L81 RCLx Q
L42 RCL J      L52 INPUT R    L62 RCLx P     L72 STO- T     L82 STO- S
L43 RCLx L     L53 INPUT S    L63 STO- Q     L73 RCL G      L83 RCL J
L44 STO- O     L54 INPUT T    L64 RCL C      L74 STOx R     L84 RCLx Q
L45 0          L55 RCL A      L65 RCLx P     L75 STOx S     L85 STO- T
L46 STO i      L56 STOx P     L66 STO- R     L76 STOx T     L86 RCL M
L47 STO F      L57 STOx Q     L67 RCL D      L77 RCL H      L87 STOx S
L48 STO K      L58 STOx R     L68 RCLx P     L78 RCLx Q     L88 STOx T
L49 STO L      L59 STOx S     L69 STO- S     L79 STO- R     L89 RCL N
L50 INPUT P    L60 STOx T     L70 RCL E      L80 RCL I      L90 RCLx R

L91 STO- S     L101 RCL O     L111 STO J     L121 RTN 
L92 RCL O      L102 RCL- N    L112 RCLx B
L93 RCLx R     L103 RCL/ M    L113 RCL+ D
L94 STO- T     L104 STO  O    L114 RCL+ C
L95 RCL S      L105 STOx H    L115 STO- E
L96 STO/ T     L106 STOx C    L116 RCL T
L97 RCL T      L107 RCL J     L117 RCL O
L98 STOx N     L108 RCL- I    L118 RCL J
L99 STOx I     L109 RCL- H    L119 RCL E
L100 STOx D    L110 RCL/ G    L120 RCL/ A