Here is some code for the 33s (originally written for the 32sii) for solving a 3x3 linear system of equations.

The code uses Cramer's rule ( with determinants) and does not change the coefficients.

Solve a 3 x 3 system of linear equationsA*X + B*Y + C*Z = D

E*X + F*Y + G*Z = H

I*X + J*Y + K*Z = LDET =

|A B C|

|E F G|

|I J K|

=

A * (F K - G J) - E * (B K - C J) + I * (B G - C F)D_X =

|D B C|

|H F G|

|L J K|Same for D_Y and D_Z

x = D_X/DET,, ...

===============================================================================

S: do via determinants and column swapping

(20 steps, 43.5, E8A7):LBL S

XEQ U; STO W; VIEW W

1; XEQ V; XEQ U; RCL/ W; STO X; 1; XEQ V

2; XEQ V; XEQ U; RCL/ W; STO Y; 2; XEQ V

3; XEQ V; XEQ U; RCL/ W; STO Z; 3; XEQ V

RTNU: determinant of [ [a, b, c], [e, f, g], [i, j, k] ]

(33.0, A5DB)LBL U

// DET = A * (F K - G J) - E * (B K - C J) + I * (B G - C F)

RCL F; RCL* K; RCL G; RCL* J; -; RCL* A;

RCL B; RCL* K; RCL C; RCL* J; -; RCL* E; -

RCL B; RCL* G; RCL C; RCL* F; -; RCL* I; +

RTNV: swap column in x reg (1..3) with [d, h, l]

(24.0, 8BD5)LBL V

STO i;

RCL D; X<> (i); STO D;

4; STO+ i;

RCL H; X<> (i); STO H;

4; STO+ i;

RCL L; X<> (i); STO L;

RTNI: input a 3x3 system (also uses lbl J)

lbl I

1.012 STO I

LBL J

INPUT (I)

ISG I

GTO J

RTN