Substitute ${\epsilon }_y=-703.125 \mu \epsilon$ into one of the equations and compute ${\gamma }_{xy}$:

${\epsilon }_y(0.64)+{\gamma }_{xy}(0.48)=+550\mu \epsilon$

$(-703.125\mu \epsilon )(0.64)+{\gamma }_{xy}(0.48)=+550\mu \epsilon$

${\gamma }_{xy}(0.48)=550\mu \epsilon -(-450\mu \epsilon )=+1,000\mu \epsilon$