Simultaneous Equation with 4 variables, can it be don?

1. Aug 30, 2008

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?

2. Aug 30, 2008

Redbelly98

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

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

3. Aug 30, 2008

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 dont 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 definetly 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 gonna 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.

4. Aug 31, 2008

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.

5. Aug 31, 2008

CRGreathouse

Pari solves this with
Code (Text):
matsolve([1,0,1,0;1,1,4,1;-1,-1,4,4;2,1,0,4],[5;12;-1;4])

6. Aug 31, 2008

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?

7. Aug 31, 2008

dan_fmx

What is Pari?

8. Aug 31, 2008

Defennder

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

9. Aug 31, 2008

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

10. Aug 31, 2008