Use the Substitution $u = \frac { 1 } { x } \text { and } v = \frac { 1 } { y }$

Use the substitution $u = \frac { 1 } { x } \text { and } v = \frac { 1 } { y }$ to rewrite the equations in the system in terms of the variables u and
v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original
system in terms of x and y.
- $$\begin{array} { l } \frac { 2 } { x } + \frac { 1 } { y } = - 4 \\\frac { 2 } { x } - \frac { 3 } { y } = 20\end{array}$$

A) $\{ ( 1 , - 6 ) \}$
B) $\left\{ \left( - \frac { 5 } { 2 } , 1 \right) \right\}$
C) $\left\{ \left( 1 , - \frac { 1 } { 6 } \right) \right\}$
D) $\left\{ \left( - \frac { 2 } { 5 } , 1 \right) \right\}$