\[ \left[ \begin{array}{c}
x \\
y \\ \end{array} \right] \] = -\frac{1}{b(1+a)} adj \Bigg(\[ \left[ \begin{array}{cc}
1 &  b \\
a  & -b \\ \end{array} \right] \]\Bigg)  \[ \left[ \begin{array}{c}
0 \\
b \\ \end{array} \right] \]