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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. $1$
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