Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Hi I have these equations that I wish to know how to reach the variables

for example

A=6 D=A-C B=2C

All I have is the value of A, and A changes from time to time so its not always 6 it can be 8, 20 or anything else.

How can I get the values of each B, C, and D?

Note that, all numbers have to be integer, no floats.

share|improve this question
    
Your system of equations is underdetermined. Even if restricting to integers, there can be more than one solution. $(A,B,C,D)=(6,12,6,0)$ is a solution, but so is $(A,B,C,D)=(6,8,4,2)$. You have to provide us a bit more background. Especially about the time dependency, which probably contains extra information. –  Raskolnikov Jan 11 '11 at 15:58

2 Answers 2

To put it simply, you can't. You have 3 linear equations for 4 variables, so you have an underdetermined linear system which admits infinitely many solutions. To use your example, $D$ and $B$ depend entirely on $A$ and $C$. $A$ is fixed, but $C$ is not. Arbitrary choice of $C$ gets you a different set of solutions in the integers. You need more information if you want a single solution.

share|improve this answer

There is no unique solution to the system.

You essentially have two equations in three unknowns: \begin{align*} C + D &= A\\ B - 2C &= 0. \end{align*} Given a value of $A$, if you pick any value for $D$, then this will give you a value for $C$, which in turn will give you a value for $B$. Or you can pick any value for $C$, then solve for $D$ and $B$. (You can also pick a value for $B$, so long as it is even, and get a value for $C$ and $D$).

Even if you require all values to be positive integers, there is still no unique solution: $D$ gets restricted to only the values $1$, $2,\ldots,A-1$, but each of those values will give you a valid solution with $C$ and $B$ positive integers; so the only case where you would have a unique solution in positive integers is if $A=2$ (in which case, $B=2$ and $C=D=1$).

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.