$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 1 x +2 y =-4\\ -1 x +2 y = 5 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}1\ & 2 \\ -1&2 \\ \end{array}= 1 \cdot 2 -2 \cdot \left(-1\right)=4 \\ D_x=\begin{array}{|cc|}-4\ & 2 \\ 5&2 \\ \end{array}= -4 \cdot 2 -2 \cdot 5=-18 \\ D_y=\begin{array}{|cc|}1\ & -4 \\ -1&5 \\ \end{array}= 1 \cdot 5 -\left(-4\right) \cdot \left(-1\right)=1 \\ \ x=\frac{-18}{4} \\ x=-4\frac{1}{2} \\ y=\frac{1}{4} \\ y=\frac{1}{4} \\ L=\{-4\frac{1}{2}/\frac{1}{4}\}\\ \, \end{array}$