$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ -\frac{1}{2} x +4 y =6\\ -2 x -8 y = 2 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}-\frac{1}{2}\ & 4 \\ -2&-8 \\ \end{array}= -\frac{1}{2} \cdot \left(-8\right) -4 \cdot \left(-2\right)=12 \\ D_x=\begin{array}{|cc|}6\ & 4 \\ 2&-8 \\ \end{array}= 6 \cdot \left(-8\right) -4 \cdot 2=-56 \\ D_y=\begin{array}{|cc|}-\frac{1}{2}\ & 6 \\ -2&2 \\ \end{array}= -\frac{1}{2} \cdot 2 -6 \cdot \left(-2\right)=11 \\ \ x=\frac{-56}{12} \\ x=-4\frac{2}{3} \\ y=\frac{11}{12} \\ y=\frac{11}{12} \\ L=\{-4\frac{2}{3}/\frac{11}{12}\}\\ \, \end{array}$