system of linear equations

[travelmail26]

I'd like some help solving a simple system of linear equations. Here is an example:

- solve, a + b + c + d = 100
- a > (b + c)
- b = c
- c > d

In this case, I want to find values for a, b, c and d. "a" is the highest rank, b and c are rank 2 and d is rank 3. All of the variables added together should equal 100. all variables are positive real numbers.

How do I solve this system of linear equations and find a fixed value for each variable?

Thank you and please let me know if I can make this question more clear. It's been a while since I've done linear algebra and any help solving (and showing how to get the answer) is very helpful.

 

[lev888]

Combined Linear Systems of Equations and Inequalities - Expii

When a system includes both equations and inequalities, its solutions are the intersection of all possible solutions to the equations (lines) and all possible solutions to the inequalities (shaded areas). As another option, you could first substitute or eliminate away a variable in one of the...

www.expii.com

 

[topsquark]

I'd like some help solving a simple system of linear equations. Here is an example:

- solve, a + b + c + d = 100
- a > (b + c)
- b = c
- c > d

In this case, I want to find values for a, b, c and d. "a" is the highest rank, b and c are rank 2 and d is rank 3. All of the variables added together should equal 100. all variables are positive real numbers.

How do I solve this system of linear equations and find a fixed value for each variable?

Thank you and please let me know if I can make this question more clear. It's been a while since I've done linear algebra and any help solving (and showing how to get the answer) is very helpful.

Let's get rid of a variable and just set c = b. Then we have a + 2b + d = 100 and a > 2b and b > d.

d = 100 - a - 2b. So a > d means that a > 100 - a - 2b. Then we have a > 50 - b.

So d = 100 - a - 2b and a > 50 - b and a > 2b and b > d.

That's the best I can do to whittle it down. There is more than one possible solution. Play with it a bit. For example I get (a, b, d) = (45, 20, 15) and (a, b, d) = (48, 21, 10) as solutions.

-Dan

 

[Deleted member 4993]

I'd like some help solving a simple system of linear equations. Here is an example:

- solve, a + b + c + d = 100
- a > (b + c)
- b = c
- c > d

In this case, I want to find values for a, b, c and d. "a" is the highest rank, b and c are rank 2 and d is rank 3. All of the variables added together should equal 100. all variables are positive real numbers.

How do I solve this system of linear equations and find a fixed value for each variable?

Thank you and please let me know if I can make this question more clear. It's been a while since I've done linear algebra and any help solving (and showing how to get the answer) is very helpful.

You cannot calculate a unique set of values assigned to a, b, c and d - from given set of equations.

For example: {a, b, c, d) could be (95, 2, 2, 1) ......or.... (92, 3, 3, 2) and many more (assuming a, b, c & d

Please post the exact problem you want solve

 

[Steven G]

Please do not put a '-' at the start of each line. You do know that it looks a bit like a negative sign.
In fact, if the 1st line, which was a sentence, did not have a - sign at the beginning me and everyone else would have misread the last three lines of you post.

 

[Steven G]

You cannot calculate a unique set of values assigned to a, b, c and d - from given set of equations.

You are correct! Might it be that the OP did not post a set of equations?

 

[Steven G]

An equation has an equal sign. Since some of your statements have > signs they are called inequalities.

 

[JeffM]

I hesitate to disagree with other helpers, who frequently know much more than I do.

If we are talking about real solutions, we need at least n independent and consistent equations to solve for n unknowns.

But you did not give us n equations.

If, on the other hand, we are talking about integer solutions, we may be able to solve for n unknowns with fewer than n equations because we have extra information. Unfortunately, this branch of mathematics is not fully explored. You need to provide every scrap of relevant information.