(15C) Three Linear Equations in Three Unknowns

[Gamo]

This program solve for Simultaneous Equation in Three Unknowns.

Formula used Cramer’s Rule for a 3×3 System (with Three Variables)

Equations:

a1(X) + b1(Y) + c1(Z) = d1
a2(X) + b2(Y) + c2(Z) = d2
a3(X) + b3(Y) + c3(Z) = d3

------------------------------------
Procedure:

[E] Initialize Display 0.000000000 briefly then 0.0000

a1 [ENTER] a2 [ENTER] a3 [R/S]
b1 [ENTER] b2 [ENTER] b3 [R/S]
c1 [ENTER] c2 [ENTER] c3 [R/S]
d1 [ENTER] d2 [ENTER] d3 [R/S]

[D] Answer Determinant // If 0 "No Solution"
[A] Answer X
[B] Answer Y
[C] Answer Z

--------------------------------------
Example:

x - 8y + z = 4
-x + 2y + z = 2
x - y + 2z = -1

[E] 0.000000000 briefly then 0.00 // Initialize

1 [ENTER] 1 [CHS] [ENTER] 1 [R/S] display 1
8 [CHS] [ENTER] 2 [ENTER] 1 [CHS] [R/S] display -8
1 [ENTER] 1 [ENTER] 2 [R/S] display 1
4 [ENTER] 2 [ENTER] 1 [CHS] [R/S] display 4

[D] display -20.0000 // Determinant
[A] display -3.0000 // Answer X
[B] display -0.8000 // Answer Y
[C] display 0.6000 // Answer Z

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Program:

Set Memory Reallocation as needed by this program.

13 f [DIM] [(i)]

Check to see require Memory Usage have set correctly

Press g then press and hold [MEM] display 13 14 24-4

Code:


LBL E   // Initialize and Store Elements
REG
CLx
FIX 9 
PSE
FIX 4
R/S
STO 3
Rv
STO 2
Rv
STO 1
R/S
STO 6
Rv
STO 5
Rv
STO 4
R/S
STO 9
Rv
STO 8
Rv
STO 7
R/S
STO .3
Rv
STO .2
Rv
STO .1
RTN
----------------------------
LBL D   // Determinant
RCL 5
RCL 9
  x
RCL 8
RCL 6
  x
  -
RCL 1
  x
RCL 2
RCL 9
  x
RCL 8
RCL 3
  x
  -
RCL 4
  x
  -
RCL 2
RCL 6
  x
RCL 5
RCL 3
  x
  -
RCL 7
  x
  +
STO 0  
---------------------------
LBL A   // Find X
RCL 5
RCL 9
  x
RCL 8
RCL 6
  x
  -
RCL .1
  x
RCL .2
RCL 9
  x
RCL 8
RCL .3
  x
  -
RCL 4
  x
  -
RCL .2
RCL 6
  x
RCL 5
RCL .3
  x
  -
RCL 7
  x
  +
RCL 0
  ÷
RTN
----------------------------
LBL B   // Find Y
RCL .2
RCL 9
  x
RCL 8
RCL .3
  x
  -
RCL 1
  x
RCL 2
RCL 9
  x
RCL 8
RCL 3
  x
  -
RCL .1
  x
  -
RCL 2
RCL .3
  x
RCL .2
RCL 3
  x
  -
RCL 7
  x
  +
RCL 0
  ÷
RTN
-------------------------
LBL C   // Find Z
RCL 5
RCL .3
  x
RCL .2
RCL 6
  x
  -
RCL 1
  x
RCL 2
RCL .3
  x
RCL .2
RCL 3
  x
  -
RCL 4
  x
  -
RCL 2
RCL 6
   x
RCL 5
RCL 3
  x
  -
RCL .1
  x
  +
RCL 0
  ÷
RTN

Gamo