A solution (x,y) of the system of equations $x-y=\frac{1}{3}and{\cos }^2\left(\pi x\right)-{\sin }^2\left(\pi y\right)=\frac{1}{2}$  is given by

• A

  $\left\{\frac{7}{6},\frac{5}{6}\right\}$

• B

  $\left\{\frac{2}{3},\frac{1}{3}\right\}$

• C

  $\left\{\frac{-2}{3},-\frac{1}{3}\right\}$

• D

  $\left\{\frac{1}{6},\frac{5}{6}\right\}$