Deriving Equation x1m=(x1CMC2)/(x1CMC2+x2CMC1) | Tinkering with Equations

[jajajujujojo]

1. Please could you give me a hand with deriving the following equation:

x₁^m=(x₁CMC₂)/(x₁CMC₂+x₂CMC₁)

Homework Equations

Eq 1: 1/CMC=x₁/CMC₁+x₂/CMC₂
Eq 2: CMC=x₁^mCMC₁+x₂^mCMC₂
Eq 3: x₁+x₂=1

The Attempt at a Solution

[/B]
1. invert Eq 2 and equate with Eq 1.
2. eliminate x₂^m using the fact that x₂^m=(1-x₁^m)
3. Rearrange..

I get to the following and don't know how to get closer to the solution. I've got a feeling I'm missing something obvious.

x₁^m=[(CMC₁/x₁)+(CMC₂/x₂)-CMC₂)]/(CMC₁-CMC₂)

Please help!

Thank you in advance.

 

[Mark44]

1. Please could you give me a hand with deriving the following equation:

x₁^m=(x₁CMC₂)/(x₁CMC₂+x₂CMC₁)

Homework Equations

Eq 1: 1/CMC=x₁/CMC₁+x₂/CMC₂
Eq 2: CMC=x₁^mCMC₁+x₂^mCMC₂
Eq 3: x₁+x₂=1

The Attempt at a Solution

[/B]
1. invert Eq 2 and equate with Eq 1.
2. eliminate x₂^m using the fact that x₂^m=(1-x₁^m)
3. Rearrange..

Please show the work that you have done. Telling us a result you have gotten to does not help us understand where you might have gone astray.

I get to the following and don't know how to get closer to the solution. I've got a feeling I'm missing something obvious.

x₁^m=[(CMC₁/x₁)+(CMC₂/x₂)-CMC₂)]/(CMC₁-CMC₂)

Please help!

Thank you in advance.

 

[Chestermiller]

What are you ultimately trying to solve for?

You can solve for x1 and x2 immediately by working exclusively with eqns. 1 and 3. The equations are linear.

Chet

 

[BvU]

the fact that x2^m = ( 1 - x1^m )

Is based on what, exactly ?

And: you say you want help in deriving these equations. You mean solving ?