How do you solve the system of equations(adsbygoogle = window.adsbygoogle || []).push({});

[tex]e^{x_{1}+y_{1}}+e^{x_{1}+y_{2}}=a_{1}[/tex]

[tex]e^{x_{2}+y_{1}}+e^{x_{2}+y_{2}}=a_{2}[/tex]

[tex]e^{x_{1}+y_{1}}+e^{x_{2}+y_{1}}=b_{1}[/tex]

[tex]e^{x_{1}+y_{2}}+e^{x_{2}+y_{2}}=b_{2}[/tex]

x1, x2, y1, y2 are the variables for which I want to solve the equations, a1, a2, b1, b2 are known.

Context: I need to solve this in order to get the unknown maximum entropy joint probabilities

[tex]p_{ij}=e^{-1-x_{i}-y_{j}}[/tex]

[tex]\mbox{for the known marginal probabilities (}a_{i}\mbox{ and }b_{j}\mbox{).}[/tex]

i know there is way to do this in information theory, but I need to solve it algebraically.

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# 4 equations, 4 variables

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