 (12C Platinum) Three Linear Equations in Three Unknowns - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: General Software Library (/forum-13.html) +--- Thread: (12C Platinum) Three Linear Equations in Three Unknowns (/thread-11909.html) (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 2 This 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