$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 8 x -3 y =10\\ 12 x -5 y = 24 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}8\ & -3 \\ 12&-5 \\ \end{array}= 8 \cdot \left(-5\right) -\left(-3\right) \cdot 12=-4 \\ D_x=\begin{array}{|cc|}10\ & -3 \\ 24&-5 \\ \end{array}= 10 \cdot \left(-5\right) -\left(-3\right) \cdot 24=22 \\ D_y=\begin{array}{|cc|}8\ & 10 \\ 12&24 \\ \end{array}= 8 \cdot 24 -10 \cdot 12=72 \\ \ x=\frac{22}{-4} \\ x=-5\frac{1}{2} \\ y=\frac{72}{-4} \\ y=-18 \\ L=\{-5\frac{1}{2}/-18\}\\ \, \end{array}$