Simultaneous Equation with 4 variables, can it be don?

[dan_fmx]

Hi

I am doing integration work in maths c. I have simplified the equation using long division however when I equated the answers, i got 4 simultaneous equations with 4 variables.

My equations are:

A + C = 5
A + B + 4C + D = 12
-A -B + 4C + 4D = -1
2A + B + 4D = 4

Can this be done?

 

[Redbelly98]

Yes, in general. Occasionally, such a system will have no solution.

You could use the techniques of elimination and/or substitution.

 

[lax1113]

Hello,
Wow, this is the first time i have ever gotten to answer a question! Like the gentlemen above me said, substituting to try to eliminate variables does work, it is very annoying, and took a couple pieces of paper, but i ended up getting an answer. The key is that first equation, since it only has two variables, if you can solve for one of them variabes down the road, you will knock off an entire one. Also, I don't know if you have one, but TI 89's have a simultaneous equation solver that works awesome, real easy to use, which is how i checked my answer. Just do some substituting to solve for a certain variable and you'll definately get it in time. we had a problem like this in math last year for extra credit, never showed us how to do it, just gave it to us... Nobody got it I'm going to not put up the answers, because it should be worked out, but if you can't get it and nobody else can give you better help soon, let me know, i'll send you the numbers.

 

[Defennder]

If you're familiar with elementary linear algebra you could put all those equations into a matrix and use the Gauss-Jordan elimination to find the reduced-row echelon form, it's quicker than having to use substitution and elimination by hand.

 

[CRGreathouse]

Pari solves this with

matsolve([1,0,1,0;1,1,4,1;-1,-1,4,4;2,1,0,4],[5;12;-1;4])

 

[dan_fmx]

Hey I have just looked on the TI site and found a poly nomial simultaneous equation solver and found these values. Can you tell me if you got the same? I got A=3, B=2, C=2 and D=-1. I dare say the teacher will want me to show working so the only thing I could really do is spend a nice long day of simultaneous equating?

 

[dan_fmx]

Pari solves this with

matsolve([1,0,1,0;1,1,4,1;-1,-1,4,4;2,1,0,4],[5;12;-1;4])

What is Pari?

 

[Defennder]

Hey I have just looked on the TI site and found a poly nomial simultaneous equation solver and found these values. Can you tell me if you got the same? I got A=3, B=2, C=2 and D=-1. I dare say the teacher will want me to show working so the only thing I could really do is spend a nice long day of simultaneous equating?

You can easily check by substituting these values into your original equations.

 

[dan_fmx]

I ended up using Gausian Elemination for the assignment and I got the same values. I know that people in the class have used the substitution method but substituiton is just impracticle and I don't have enough patients.

Thanks for all the help and ideas on how to do it

Dan

 

[CRGreathouse]

What is Pari?

A very powerful calculator focused on number theory.
http://pari.math.u-bordeaux.fr/