$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 4 x +6 y =7\\ 5 x +6 y = 5 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}4\ & 6 \\ 5&6 \\ \end{array}= 4 \cdot 6 -6 \cdot 5=-6 \\ D_x=\begin{array}{|cc|}7\ & 6 \\ 5&6 \\ \end{array}= 7 \cdot 6 -6 \cdot 5=12 \\ D_y=\begin{array}{|cc|}4\ & 7 \\ 5&5 \\ \end{array}= 4 \cdot 5 -7 \cdot 5=-15 \\ \ x=\frac{12}{-6} \\ x=-2 \\ y=\frac{-15}{-6} \\ y=2\frac{1}{2} \\ L=\{-2/2\frac{1}{2}\}\\ \, \end{array}$