$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 2 x -7 y =-8\\ 7 x -1 y = -9 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}2\ & -7 \\ 7&-1 \\ \end{array}= 2 \cdot \left(-1\right) -\left(-7\right) \cdot 7=47 \\ D_x=\begin{array}{|cc|}-8\ & -7 \\ -9&-1 \\ \end{array}= -8 \cdot \left(-1\right) -\left(-7\right) \cdot \left(-9\right)=-55 \\ D_y=\begin{array}{|cc|}2\ & -8 \\ 7&-9 \\ \end{array}= 2 \cdot \left(-9\right) -\left(-8\right) \cdot 7=38 \\ \ x=\frac{-55}{47} \\ x=-1\frac{8}{47} \\ y=\frac{38}{47} \\ y=\frac{38}{47} \\ L=\{-1\frac{8}{47}/\frac{38}{47}\}\\ \, \end{array}$