Let $x,y\in R,x>0,y>0$  satisfying the system of equations  $x^{{\log }_{y}x}.y=x^{\frac{3}{2}}$ and  ${\log }_{4}y.{\log }_y(y-3x)=1.$ Then which of the following is true

Value of x satisfying system of equations is irrational

Value of x satisfying system of equations is rational

No values of x and y satisfy the system of equations

Exactly one pair of  $(x,y)$ satisfy the system of equations