$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 3 x +5 y =19\\ 7 x +5 y = 31 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}3\ & 5 \\ 7&5 \\ \end{array}= 3 \cdot 5 -5 \cdot 7=-20 \\ D_x=\begin{array}{|cc|}19\ & 5 \\ 31&5 \\ \end{array}= 19 \cdot 5 -5 \cdot 31=-60 \\ D_y=\begin{array}{|cc|}3\ & 19 \\ 7&31 \\ \end{array}= 3 \cdot 31 -19 \cdot 7=-40 \\ \ x=\frac{-60}{-20} \\ x=3 \\ y=\frac{-40}{-20} \\ y=2 \\ L=\{3/2\}\\ \, \end{array}$