For the case of plane stress, show that Hooke's law can be written as [sigma_{x}=frac{E}{left(1-u^{2} ight)}left(epsilon_{x}+u epsilon_{y}

For the case of plane stress, show that Hooke's law can be written as

\[\sigma_{x}=\frac{E}{\left(1-u^{2}\right)}\left(\epsilon_{x}+u \epsilon_{y}\right), \quad \sigma_{y}=\frac{E}{\left(1-u^{2}\right)}\left(\epsilon_{y}+u \epsilon_{x}\right)\]