Simultaneous Equation Solver HP 33s


To me the most important programs are the root finder and simultaneous equation solver (SES). I used the books program for the root finder and I'm low on variables left to creat a program for the SES. Does anyone have a short program version for SES or the root finder? Please help, must have both programs!



What magnitude of a matrix do you wish to solve? A 2-eqn / 2-unknown is simple (I posted one in the software for 32sii here in the museum). However, I haven't tried a 3&3, or greater yet. I have an nxn solver that I wrote in 'c', but that does us no good, I fear.

Yep, wish one could create multi-character variables on the 33s...


I'm looking for a 3x3 solver. I'm only using it to solve variables for situations when you have three equations with unkown variables for each equation (huge time saver). Thanks for the response and please let me know if you find anything!


A 3x3 is really trivial to implement. However, no matter how you do it, you are going to need 9 variables and more like 12 if you want to make it easier to use and manipulate. 15 if you don't want to destroy your existing variables or data (may need 15 anyway, if you don't make great use of the stack).

I suggest Cramers rule for finding determinets and staying with only using 9 variables (actually 10, you should store the determinet as well, rather than trust the stack). Although somewhat awkward, will only use 9 variables and will allow you to find value for whichever unknown you wish. If you need all three unknowns, you run the program 4 times, if you just need one, you run it twice.

Sadly, this is the limitation of 27 variables.

An Hp32s/32sii/33s just can't compare to a calculator such as the Hp42s. If you had one, it makes it even MORE difficult to use an Hp33s (I don't cry, I am not quite that emotional, but the Hp33s ain't no big leap. If people were evolving like calculators, we'd all be chimps about now! Hey wait a minute, I resemble that remark! 8o) )

Unfortunately, my batteries need changing on my 42s last week and YOU GUESSED IT! I lost several K of programs. Its to bad there was no serial port on the 42s. That, 32K and a units conversion feature like the 48G and I would never need another pocket calculater, nor would I ever look for one! But I guess marketing wins out, because then HP only makes ONE SALE!

Actually the Hp17Bii doesn't suffer from variable limitations, but it Ain't allowed on the NCEES exams either.


I'm only using the HP 33s b/c I'm taking the PE Exam next month. I don't have experience in writing programs. Do you have a 3x3 program (perhaps using Cramers Rule) written that you could share?


Here is a program written by Walter Grey that will work aside from storing into registers, you will store into alpha variables.

Any good EE book (That's my introduction to Cramer) will explain the method in more detail, but the program above should work. Post if you have any problems.

I too hope to take the PE this spring, but my credentials are being reviewed since I do not have an Engineering degree. I am under a bit more scrutiney.


I don't know if program above will work as I looked over quickly.

The steps below will work for a 3x3 to make a det

|a b c|
|d e f|
|g h i|

(axexi + bxfxg + cxdxh) - (axfxh + bxdxi + cxexg)

The final number is the determinant for the matrix.

now include your values of the equations into the row (replace) that you wish to find the unknown (assuming x is first row, y is second, z is third) and crunch out the next determinant.

now you have two determinants. Divide your 2nd determinant by the first one and you will have the answer to the unknown of whichever row you had substituted for.

The programming is straightforward, just store and recall variable as you crank out the values and let them move on the stack as you would a typical calculation.


JJJ --

The HP-20S has a 99-line built-in Cramer's Rule solver for 3x3 linear systems, which can also be used for 2x2 systems. The 20S is not approved by NCEES, although it meets standards.

For adapting the routine to the 33S, each numerical storage register and numerical label would have to be replaced by single-letter values. The 20S is algebraic. Adapting the routine for 33S Algebraic mode might be easier.

-- KS

Edited: 3 Mar 2005, 10:21 p.m.


The Hp33s has the programming routine in its manual in chapter 15 pgs 16-17. I believe the RCL x Alpha is wrong and should be RCL Alpha x in the manual. That worked for me, I did not use the program listed in the manual.



Botht the 11c manual, and the 32sii manual have 3 x 3 matrix programs for solving simultaneous equations. There may be another routine in the 11c "solutions handbook" which I have at home. Actually, I see now that the 11c has tow different programs--a cramers rule method ofr solving equations, as well as a matrix manipulation program.

Go the the HP website and download the manual for the 32sii. As the 33s is a new version of the 32sii, you should be able to take the program almost exactly as it is (just do not pay any attention to the checksums and bytes--the machines use different architecture).

The 11c, while much older, also has programs that are fully compatible on the 33s, excetp that you will change the numbered registers to letter variables.

I would be happy to fax you all of these---I'll send you an e-mail, and you can e-mail me your fax number.




Your state board should allow you to bring two 33S calculators to the PE exam. You could store the root finder program in one and the SES in another.

Alternatively, supplement your 33S with a Casio FX-115MS Plus, which is NCEES-approved for the PE exam and only costs about $15. It is non-programmable, but it has built-in features for solving 2x2 and 3x3 simultaneous equations, as well as roots of quadratic and cubic equations.


I didn't know the Casio FX-115MS (which is my planned backup) could handle a 3x3.


I don't actually have a Casio FX-115MS or FX-115MS Plus myself, but I looked at the manual, which is online at:

Simultaneous linear equations with three unknowns are addressed on pages 24-25.


Casio is good, or try Sharp EL506WBBK Solar that has all the features of Casio FX-115MS Plus -- AND four 4x4 matrix, AND four continuous formula memories, AND 52 constants+42 conversions, AND true edit/replay rather than backspace and rekey. It is also $15. It's a pity HP isn't marketing inexpensive machines like it.


And its not listed on the NCEES approved calculator list. Without being approved, it will just be collected by the proctor. It matters not how similiar or feature rich or poor it may be. Only a half dozen calculator models are allowed. Anything else, isn't.


Hi Norris. This is an excellent suggestion. The Casio is a decent scientific calculator with dual power, a nice two line display (one LCD segments, the other dots) with , or . separating the 000's and it has the desired 2x2 and 3x3 equation solver. Also, you can use one to check the answers from the other ;-)




Here is the math for solving a 3x3 system of linear equations. I generated the output using MATLAB.

A= [A11 A12 A13;A21 A22 A32; A31 A32 A33]

B is the solution ccolumn vector
B= [B1;B2;B3]

Det = (A11*A33*A22-A33*A21*A12-A31*A13*A22+A31*A12*A32+A32*A21*A13-A11*A32^2)

X(1) = -(-A12*A32*B3+A12*B2*A33-A13*A32*B2+A13*B3*A22-B1*A33*A22+B1*A32^2)/ Det

X(2) = (-A11*A32*B3+A11*B2*A33+A21*A13*B3-B2*A31*A13+A32*A31*B1-A21*B1*A33)/ Det

X(3) = (-A31*B1*A22-A11*A32*B2+A11*B3*A22-B3*A21*A12+A31*A12*B2+A32*A21*B1)/ Det

Hope this helps!


Possibly Related Threads...
Thread Author Replies Views Last Post
  hp-prime solver and variable name fabrice48 22 2,522 12-10-2013, 03:25 AM
Last Post: fabrice48
  Solver issue with HP 17BII - different from 19BII Jeff Kearns 13 1,220 11-28-2013, 02:36 AM
Last Post: Don Shepherd
  HP Prime Triangle solver BruceH 29 2,479 11-28-2013, 12:03 AM
Last Post: Dale Reed
  HP prime: linear solver app Alberto Candel 1 442 11-21-2013, 01:57 AM
Last Post: Michael Carey
  HP Prime: Linear Solver app bug BruceH 0 305 11-15-2013, 06:36 PM
Last Post: BruceH
  Equation Library/App for the Prime Harold A Climer 3 547 10-30-2013, 10:14 AM
Last Post: CompSystems
  Equation Library on the PRIME Harold A Climer 0 314 10-26-2013, 10:01 AM
Last Post: Harold A Climer
  HP Prime Solver Variables Issue Anibal Morones Ruelas 8 989 10-19-2013, 09:45 AM
Last Post: Harold A Climer
  HP Prime triangle solver oddity BruceH 0 301 10-13-2013, 09:08 PM
Last Post: BruceH
  Using units in Numeric Solver Harold A Climer 1 370 10-13-2013, 10:44 AM
Last Post: Tim Wessman

Forum Jump: