$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 1 x +1 y =10\\ 1 x -1 y = 4 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}1\ & 1 \\ 1&-1 \\ \end{array}= 1 \cdot \left(-1\right) -1 \cdot 1=-2 \\ D_x=\begin{array}{|cc|}10\ & 1 \\ 4&-1 \\ \end{array}= 10 \cdot \left(-1\right) -1 \cdot 4=-14 \\ D_y=\begin{array}{|cc|}1\ & 10 \\ 1&4 \\ \end{array}= 1 \cdot 4 -10 \cdot 1=-6 \\ \ x=\frac{-14}{-2} \\ x=7 \\ y=\frac{-6}{-2} \\ y=3 \\ L=\{7/3\}\\ \, \end{array}$