12-09-2018, 12:43 PM
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
------------------------------------------------------
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
Gamo
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
------------------------------------------------------
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