$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 7 x +1\frac{1}{2} y =1\\ 2 x -5 y = 22 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}7\ & 1\frac{1}{2} \\ 2&-5 \\ \end{array}= 7 \cdot \left(-5\right) -1\frac{1}{2} \cdot 2=-38 \\ D_x=\begin{array}{|cc|}1\ & 1\frac{1}{2} \\ 22&-5 \\ \end{array}= 1 \cdot \left(-5\right) -1\frac{1}{2} \cdot 22=-38 \\ D_y=\begin{array}{|cc|}7\ & 1 \\ 2&22 \\ \end{array}= 7 \cdot 22 -1 \cdot 2=152 \\ \ x=\frac{-38}{-38} \\ x=1 \\ y=\frac{152}{-38} \\ y=-4 \\ L=\{1/-4\}\\ \, \end{array}$