$\begin{array}{l} D_h=\begin{array}{|cc|}a1\ & b1 \\ a2&b2 \\ \end{array}= a1 \cdot b2 -b1 \cdot a2 \\ D_x=\begin{array}{|cc|}c1\ & b1 \\ c2&b2 \\ \end{array}= c1 \cdot b2 -b1 \cdot c2 \\ D_y=\begin{array}{|cc|}a1\ & c1 \\ a2&c2 \\ \end{array}= a1 \cdot c2 -c1 \cdot a2\\ x=\frac{D_x}{D_h} \\ y=\frac{D_y}{D_h} \\ \\ \textbf{Gegeben:} \\ \\ 1 x +1 y =1\\ 2 x +2 y = 2 \\ \\ \\ \\ \textbf{Rechnung:} \\ D_h=\begin{array}{|cc|}1\ & 1 \\ 2&2 \\ \end{array}= 1 \cdot 2 -1 \cdot 2=0 \\ D_x=\begin{array}{|cc|}1\ & 1 \\ 2&2 \\ \end{array}= 1 \cdot 2 -1 \cdot 2=0 \\ D_y=\begin{array}{|cc|}1\ & 1 \\ 2&2 \\ \end{array}= 1 \cdot 2 -1 \cdot 2=0 \\ \ L=\{ \text{unendlich}\} \, \end{array}$