$\begin{array}{l} \text{Gegeben:} \\ a1 \cdot x +b1 \cdot y =c1\\ a2 \cdot x +b2 \cdot y =c2 \\ \\ \text{Gesucht:} \\\text{x und y} \\ \\ \textbf{Gegeben:} \\ \\ -1 x +1 y =3\\ \frac{1}{2} x -4 y = 5 \\ \\ \\ \\ \textbf{Rechnung:} \\\begin{array}{l|l} \begin{array}{l} I \qquad -1 x +1 y =3\\ II \qquad \frac{1}{2} x -4 y = 5 \\ \text{I nach y auflösen}\\ -1 x +1 y =3 \\ -1 x +1 y =3 \qquad /+1 x\\ 1 y =3 +1 x \qquad /:1 \\ y =3 +1 x \\ \text{II nach y auflösen}\\ \frac{1}{2} x -4 y =5 \\ \frac{1}{2} x -4 y =5 \qquad /-\frac{1}{2} x\\ -4 y =5 -\frac{1}{2} x \qquad /:\left(-4\right) \\ y =-1\frac{1}{4} +\frac{1}{8} x \\ \text{I = II}\\ 3 +1 x =-1\frac{1}{4} +\frac{1}{8} x \qquad /-1 x /+1\frac{1}{4} \\ 3+1\frac{1}{4} =\frac{1}{8} x -1 x \\ 4\frac{1}{4} =-\frac{7}{8} x \qquad /:\left(-\frac{7}{8}\right) \\ x=-4\frac{6}{7} \\ \text{x in I}\\ y =3 +1 \cdot -4\frac{6}{7} \\ y=-1\frac{6}{7} \\ L=\{-4\frac{6}{7}/-1\frac{6}{7}\} \end{array} & \begin{array}{l} I \qquad -1 x +1 y =3\\ II \qquad \frac{1}{2} x -4 y = 5 \\ \text{I nach x auflösen}\\ -1 x +1 y =3 \\ -1 x +1 y =3 \qquad /-1 y\\ -1 x =3 -1 y \qquad /:\left(-1\right) \\ x =-3 +1 y \\ \text{II nach x auflösen}\\ \frac{1}{2} x -4 y =5 \\ \frac{1}{2} x -4 y =5 \qquad /+4 y\\ \frac{1}{2} x =5 +4 y \qquad /:\frac{1}{2} \\ x =10 +8 y \\ \text{I = II}\\ -3 +1 y =10 +8 y \qquad /-1 y /-10 \\ -3-10 =8 y -1 y \\ -13 =7 y \qquad /:7 \\ y=-1\frac{6}{7} \\ \text{y in I}\\ x =-3 +1 \cdot -1\frac{6}{7} \\ x=-4\frac{6}{7} \\ L=\{-4\frac{6}{7}/-1\frac{6}{7}\} \end{array} \end{array} \end{array}$