Two equations Two unknowns 1

It seems you are looking for symbolic evaluations.
You will have to attach your sheet to show what you really need and want to achieve.

How can I be more clear on what I really want and want to achieve? My 2 equations are as follows:

epsilon_ys = A/E * [1+3/7*(A/R)^(n-1)]
epsilon_ts = B/E * [1+3/7*(B/R)^(n-1)

I want to write my two unknowns as functions of the knowns. The unknowns are n and R. Everything else is known. I don't want to use numbers for the knowns. I want it to be letters and symbols all the way. So, 2 equations 2 unknowns, symbols and letters all the way! No numbers!

Cheers!

So as you are looking for a symbolic solution of your system of two equations, you will have to use Mathcad's symbolics.
You can either user the symbolic solve command (you provide the two equations in a 2x1 matrix) or as an alternative you can use a solve block with find() which you evaluate symbolically (you should not provide guess values in this case).

BTW, the reason for attaching a worksheet are manyfolds. It usually more clearly shows whats needed or why an attempt went wrong. We see which version of Mathcad you are using (you haven't stated it), MC11, MC15, Prime and last but not least it makes it more convenient for people willing to help to play with a ready made sheet rather than having to type in all from scartch.

Here is the worksheet. I still need to find R, but don't know how.

Nice pic but still no worksheet.
You have to solve for both variables at the same time, but I am not sure if Mathcad will be able to provide a symbolic solution.

It looks like you made a type in your pic - according to your first post the secon eps.ys should be an eps.ts.

I still think that Mathcad will have difficulties in presenting you are closed symbolic solution because of the involved logarithms but it shouldn't be that difficult to (partly) manual derive that solution with the help of Mathcad's symbolics. I guess you already solved your system manually yourself, though.

Why do you think that you need a symbolic solution? Unless you intend to implement the solution in assembler or C embedded in a small circuit, there might be a better way to get what you want at the end using numerics.

This is a particular form of the Ramberg-Osgood (R-O) Stress-strain
equation. While it would be fantastic to have the equation's n-exponent
be found symbolically. I do not see how such a symbolical solution can be
found.

R is normally a chosen "reference strength" and it is normally taken to
be "The Yield strength, SY"

The second equation has an error because the strain corresponding to
the tensile strength is the tensile strain and not the yield strain.

I propose that the equations be solved numerically choosing R to be
SY the solve for n number

Regards,

Calculus

I must revise my previous posting to be solved
as follows:

Solve the two (2) equations on two (2) unknown
numerically be setting R = Sy and obtaining the
data for all known parameters to initiate the
iterations.

The solution for a given material at temperature
can be solved at different temperatures resulting
in n(T) and R(T).

Once n(T) and R(T) are determined, one can use
a spline interpolation to create a Ramberg-Osgood
as a function of temperature, T.

Calculus