Starting from the generalized Hooke's law, show that the equations for ${}_x$ and ${}_z$ can be reduced to

${}_x=\frac{E}{1-v^2}(lo{n}_x+vlo{n}_z)$

${}_z=\frac{E}{1-v^2}(lo{n}_z+vlo{n}_x)$

for plane stress condition in the x$-$z plane.