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(12C Platinum) Three Linear Equations in Three Unknowns - Gamo - 12-06-2018 09:38 AM
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
Detail information on how this formula work by follow this page at
https://www.chilimath.com/lessons/advanced-algebra/cramers-rule-with-three-variables/
------------------------------------
Procedure:
Input each columns from top left down.
a1 [R/S] a2 [R/S] a3 [R/S] b1 [R/S] b2 [R/S] b3 [R/S]
c1 [R/S] c2 [R/S] c3 [R/S] d1 [R/S] d2 [R/S] d3 [R/S] --> Answer
X [R/S] Y [R/S] Z
-----------------------------------
Example:
x - 8y + z = 4
-x + 2y + z = 2
x - y + 2z = -1
1 [R/S] 1 [CHS] [R/S] 1 [R/S]
8 [CHS] [R/S] 2 [R/S] 1 [CHS] [R/S]
1 [R/S] 1 [R/S] 2 [R/S]
4 [R/S] 2 [R/S] 1 [CHS] [R/S] --> -3 [R/S] -0.80 [R/S] 0.60
Answer:
X = -3
Y = -0.8
Z = 0.6
-------------------------------------
Remark:
If Determinant = 0
Display will show 0.000000000 briefly then 0.00
This indicate NO SOLUTIONS
-------------------------------------
Program: (RPN mode)
Code:
001 STO 1 // a1
002 R/S
003 STO 2 // a2
004 R/S
005 STO 3 // a3
006 R/S
007 STO 4 // b1
008 R/S
009 STO 5 // b2
010 R/S
011 STO 6 // b3
012 R/S
013 STO 7 // c1
014 R/S
015 STO 8 // c2
016 R/S
017 STO 9 // c3
018 R/S
019 STO .1 // d1
020 R/S
021 STO .2 // d2
022 R/S
023 STO .3 // d3 // Complete Input
----------------------------------
024 RCL 5
025 RCL 9
026 x
027 RCL 8
028 RCL 6
029 x
030 -
031 RCL 1
032 x
033 RCL 2
034 RCL 9
035 x
036 RCL 8
037 RCL 3
038 x
039 -
040 RCL 4
041 x
042 -
043 RCL 2
044 RCL 6
045 x
046 RCL 5
047 RCL 3
048 x
049 -
050 RCL 7
051 x
052 +
053 STO .4 // Determinant
-----------------------------------
054 X=0
055 GTO 152 // if Determinant = 0 "No Solutions"
056 RCL 5
057 RCL 9
058 x
059 RCL 8
060 RCL 6
061 x
062 -
063 RCL .1
064 x
065 RCL .2
066 RCL 9
067 x
068 RCL 8
069 RCL .3
070 x
071 -
072 RCL 4
073 x
074 -
075 RCL .2
076 RCL 6
077 x
078 RCL 5
079 RCL .3
080 x
081 -
082 RCL 7
083 x
084 +
085 RCL .4
086 ÷
087 R/S // (X)
-------------------------
088 RCL .2
089 RCL 9
090 x
091 RCL 8
092 RCL .3
093 x
094 -
095 RCL 1
096 x
097 RCL 2
098 RCL 9
099 x
100 RCL 8
101 RCL 3
102 x
103 -
104 RCL .1
105 x
106 -
107 RCL 2
108 RCL .3
109 x
110 RCL .2
111 RCL 3
112 x
113 -
114 RCL 7
115 x
116 +
117 RCL .4
118 ÷
119 R/S // (Y)
-----------------------------
120 RCL 5
121 RCL .3
122 x
123 RCL .2
124 RCL 6
125 x
126 -
127 RCL 1
128 x
129 RCL 2
130 RCL .3
131 x
132 RCL .2
133 RCL 3
134 x
135 -
136 RCL 4
137 x
138 -
139 RCL 2
140 RCL 6
141 x
142 RCL 5
143 RCL 3
144 x
145 -
146 RCL .1
147 x
148 +
149 RCL .4
150 ÷ // (Z)
151 GTO 000
-----------------------------
152 0
153 FIX 9
154 PSE
155 FIX 2This program can be use to solve for "Two Equations of Two Unknowns" as well.
Procedure:
x y 0 = c1
x y 0 = c2
0 0 1 = 1
Example:
2X - Y = 15
X + 2Y = 30
2 [R/S] 1 [R/S] 0 [R/S]
1 [CHS] [R/S] 2 [R/S] 0 [R/S]
0 [R/S] 0 [R/S] 1 [R/S]
15 [R/S] 30 [R/S] 1 [R/S] --> 12 [R/S] 9 [R/S] 1
Answer:
X = 12
Y = 9
Ignore 1
--------------------------------------------------------
Program: (ALG Mode)
Remark:
R for [RCL]
ST for [STO]
Quote:ST1 R/S ST2 R/S ST3 R/S
ST4 R/S ST5 R/S ST6 R/S
ST7 R/S ST8 R/S ST9 R/S
ST.1 R/S ST.2 R/S ST.3 // Complete Input of all elements
-------------------------------------------------------
(R5xR9)-(R8xR6)xR1 = ST.4
(R2xR9)-(R8xR3)xR4 = ST.5
(R2xR6)-(R5xR3)xR7 = ST.6
R.4 - R.5 + R.6 = ST0 // Store Determinant
-------------------------------------------------------
(R5xR9)-(R8xR6)xR.1 = ST.4
(R.2xR9)-(R8xR.3)xR4 = ST.5
(R.2xR6)-(R5xR.3)xR7 = ST.6
R.4 - R.5 + R.6 = ÷ R0 = R/S // Answer X
-------------------------------------------------------
(R.2xR9)-(R8xR.3)xR1 = ST.4
(R2xR9)-(R8xR3)xR.1 = ST.5
(R2xR.3)-(R.2xR3)xR7 = ST.6
R.4 - R.5 + R.6 = ÷ R0 = R/S // Answer Y
-------------------------------------------------------
(R5xR.3)-(R.2xR6)xR1 = ST.4
(R2xR.3)-(R.2xR3)xR4 = ST.5
(R2xR6)-(R5xR3)xR.1 = ST.6
R.4 - R.5 + R.6 = ÷ R0 = // Answer Z
Gamo