$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 9 x -2 y =5\\ 5 x -2 y = 1 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}9\ & -2 \\ 5&-2 \\ \end{array}= 9 \cdot \left(-2\right) -\left(-2\right) \cdot 5=-8 \\ D_x=\begin{array}{|cc|}5\ & -2 \\ 1&-2 \\ \end{array}= 5 \cdot \left(-2\right) -\left(-2\right) \cdot 1=-8 \\ D_y=\begin{array}{|cc|}9\ & 5 \\ 5&1 \\ \end{array}= 9 \cdot 1 -5 \cdot 5=-16 \\ \ x=\frac{-8}{-8} \\ x=1 \\ y=\frac{-16}{-8} \\ y=2 \\ L=\{1/2\}\\ \, \end{array}$