Let $a, b, c, d \in \mathbb{R}$ be such that $ad-bc \neq 0$ and $e$ be a positive number other than $1$. If $x^a y^b=e^m$, $x^c y^d=e^n$, $\Delta_1=\left|\begin{array}{ll}m & b \\ n & d\end{array}\right|$, $\Delta_2=\left|\begin{array}{ll}a & m \\ c & n\end{array}\right|$ and $\Delta_3=\left|\begin{array}{ll}a & b \\ c & d\end{array}\right|$, then the values of $x$ and $y$ are respectively.

• A
  $e^{\frac{\Delta_1}{\Delta_3}}, e^{\frac{\Delta_2}{\Delta_3}}$
• B
  $e^{\frac{\Delta_3}{\Delta_2}}, e^{\frac{\Delta_1}{\Delta_2}}$
• C
  $e^{\frac{-\Delta_1}{\Delta_3}}, e^{\frac{-\Delta_2}{\Delta_3}}$
• D
  $e^{\frac{\Delta_2}{\Delta_1}}, e^{\frac{\Delta_3}{\Delta_1}}$