Solve the System of Linear Equations $\left\{ \begin{array} { l } 3 x + 6 y = 1 \\6 x + 8 y = 2\end{array} \right.$

Multiple Choice

Solve the system of linear equations $\left\{ \begin{array} { l } 3 x + 6 y = 1 \\6 x + 8 y = 2\end{array} \right.$ using the inverse matrix $\left[ \begin{array} { c c } - \frac { 2 } { 3 } & \frac { 1 } { 2 } \\\frac { 1 } { 2 } & - \frac { 1 } { 4 }\end{array} \right]$

A) $\left[ \begin{array} { l } x \\y\end{array} \right] = \left[ \begin{array} { c } \frac { 11 } { 12 } \\0\end{array} \right]$
B) $\left[ \begin{array} { l } x \\y\end{array} \right] = \left[ \begin{array} { l } \frac { 1 } { 3 } \\0\end{array} \right]$
C) $\left[ \begin{array} { l } x \\y\end{array} \right] = \left[ \begin{array} { c } \frac { 11 } { 12 } \\\frac { 1 } { 3 }\end{array} \right]$
D) $\left[ \begin{array} { l } x \\y\end{array} \right] = \left[ \begin{array} { c } \frac { 1 } { 3 } \\- \frac { 1 } { 2 }\end{array} \right]$
E) $\left[ \begin{array} { l } x \\y\end{array} \right] = \left[ \begin{array} { c } - \frac { 1 } { 2 } \\\frac { 1 } { 3 }\end{array} \right.$