LINEAR3 hp32sII
A program to solve a linear system of 3 equations with 3 unknowns. 

System:

  Ax+By+Cz = E   (A NOT ZERO)
  Gx+Hy+Iz = K
  Mx+Ny+Oz = P

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,E, G,H,I,K, M,N,O,P.
The results for x,y,z 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 2 unknowns. 
For example, to solve a 2x2 system (x,y unknowns) enter the 
equivalent 3x3 system:

  Ax+By+0z = E   (A NOT ZERO)
  Gx+Hy+0z = K
  0x+0y+1z = 0

Memory requirements:
  Total:193.5 bytes. Program:97.5 bytes. Variables:96 bytes (8x12).
  Left free: 43.5 bytes. No Flags used.
  C CHKSUM=F0b4  097.5

x--------------x--------------x--------------x--------------x-----------
C01 LBL C      C11 INPUT M    C21 STOx P     C31 RCL B      C41 STOx O
C02 CLVARS     C12 INPUT N    C22 RCL B      C32 RCLx M     C42 STOx P
C03 INPUT A    C13 INPUT O    C23 RCLx G     C33 STO- N     C43 RCL I 
C04 INPUT B    C14 INPUT P    C24 STO- H     C34 RCL C      C44 RCLx N
C05 INPUT C    C15 RCL A      C25 RCL C      C35 RCLx M     C45 STO- O
C06 INPUT E    C16 STOx H     C26 RCLx G     C36 STO- O     C46 RCL K
C07 INPUT G    C17 STOx I     C27 STO- I     C37 RCL E      C47 RCLx N
C08 INPUT H    C18 STOx K     C28 RCL E      C38 RCLx M     C48 STO- P
C09 INPUT I    C19 STOx N     C29 RCLx G     C39 STO- P     C49 RCL O
C10 INPUT K    C20 STOx O     C30 STO- K     C40 RCL H      C50 STO/ P

C51 RCL P      C61 RCL P 
C52 STOx I     C62 RCL K 
C53 STOx C     C63 RCL E 
C54 RCL K      C64 RCL/ A
C55 RCL- I     C65 RTN  
C56 RCL/ H
C57 STO K
C58 RCLx B
C59 RCL+ C
C60 STO- E