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In the following system of equations $2^{y-x} \left(x+y \right)=1$  &  $\left(x+y \right)^{x-y}=2$ the value of $xy$ is :

1. $\frac{1}{2}$
2. $\frac{3}{4}$
3. $\frac{1}{4}$
4. $1$

1
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2
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