$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 2 x +4 y =4\\ -\frac{1}{2} x +3 y = 3 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}2\ & 4 \\ -\frac{1}{2}&3 \\ \end{array}= 2 \cdot 3 -4 \cdot \left(-\frac{1}{2}\right)=8 \\ D_x=\begin{array}{|cc|}4\ & 4 \\ 3&3 \\ \end{array}= 4 \cdot 3 -4 \cdot 3=0 \\ D_y=\begin{array}{|cc|}2\ & 4 \\ -\frac{1}{2}&3 \\ \end{array}= 2 \cdot 3 -4 \cdot \left(-\frac{1}{2}\right)=8 \\ \ x=\frac{0}{8} \\ x=0 \\ y=\frac{8}{8} \\ y=1 \\ L=\{0/1\}\\ \, \end{array}$