# Help! need to relate Antoine equation and Roaults law into coupled nonlinear equation

## Homework Statement

Given the equation for Roaults law and Antoine equation for 2 species I need to recast these into a pair of coupled non linear equations to compute the mole fraction of species one and the temperature for given values of vapor fraction and the total pressure, Antoines constants are also given.

These paired equations are eventually used in a 2x2 Jacobian so I am assuming that will have the mole fraction in terms of vapor fraction and total pressure, as well as the Temperature in terms of vapor fraction and total pressure.

## Homework Equations

Raoults Law: x(1)*P(1_sat)=y(n)*P(total)
[1-x(1)]*P(2_sat)=[1-y(1)]*P(total)
Antoine Equation: log(base10)(Psat of species i) = Ai - (Bi/(T + Ci) where Ai,Bi,Ci are constants

## The Attempt at a Solution

I have no clue how to separate these

Thank you so much for your help!!

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