$\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\frac{4}{5} x +1\frac{1}{3} y =-1\\ -\frac{2}{3} x +\frac{1}{9} y = 9 \\ \\ \\ \\ \textbf{Rechnung:} \\\begin{array}{l|l} \begin{array}{l} I \qquad -1\frac{4}{5} x +1\frac{1}{3} y =-1\\ II \qquad -\frac{2}{3} x +\frac{1}{9} y = 9 \\ \text{I nach y auflösen}\\ -1\frac{4}{5} x +1\frac{1}{3} y =-1 \\ -1\frac{4}{5} x +1\frac{1}{3} y =-1 \qquad /+1\frac{4}{5} x\\ 1\frac{1}{3} y =-1 +1\frac{4}{5} x \qquad /:1\frac{1}{3} \\ y =-\frac{3}{4} +1\frac{7}{20} x \\ \text{II nach y auflösen}\\ -\frac{2}{3} x +\frac{1}{9} y =9 \\ -\frac{2}{3} x +\frac{1}{9} y =9 \qquad /+\frac{2}{3} x\\ \frac{1}{9} y =9 +\frac{2}{3} x \qquad /:\frac{1}{9} \\ y =81 +6 x \\ \text{I = II}\\ -\frac{3}{4} +1\frac{7}{20} x =81 +6 x \qquad /-1\frac{7}{20} x /-81 \\ -\frac{3}{4}-81 =6 x -1\frac{7}{20} x \\ -81\frac{3}{4} =4\frac{13}{20} x \qquad /:4\frac{13}{20} \\ x=-17\frac{18}{31} \\ \text{x in I}\\ y =-\frac{3}{4} +1\frac{7}{20} \cdot -17\frac{18}{31} \\ y=-24\frac{15}{31} \\ L=\{-17\frac{18}{31}/-24\frac{15}{31}\} \end{array} & \begin{array}{l} I \qquad -1\frac{4}{5} x +1\frac{1}{3} y =-1\\ II \qquad -\frac{2}{3} x +\frac{1}{9} y = 9 \\ \text{I nach x auflösen}\\ -1\frac{4}{5} x +1\frac{1}{3} y =-1 \\ -1\frac{4}{5} x +1\frac{1}{3} y =-1 \qquad /-1\frac{1}{3} y\\ -1\frac{4}{5} x =-1 -1\frac{1}{3} y \qquad /:\left(-1\frac{4}{5}\right) \\ x =\frac{5}{9} +\frac{20}{27} y \\ \text{II nach x auflösen}\\ -\frac{2}{3} x +\frac{1}{9} y =9 \\ -\frac{2}{3} x +\frac{1}{9} y =9 \qquad /-\frac{1}{9} y\\ -\frac{2}{3} x =9 -\frac{1}{9} y \qquad /:\left(-\frac{2}{3}\right) \\ x =-13\frac{1}{2} +\frac{1}{6} y \\ \text{I = II}\\ \frac{5}{9} +\frac{20}{27} y =-13\frac{1}{2} +\frac{1}{6} y \qquad /-\frac{20}{27} y /+13\frac{1}{2} \\ \frac{5}{9}+13\frac{1}{2} =\frac{1}{6} y -\frac{20}{27} y \\ 14\frac{1}{18} =-\frac{31}{54} y \qquad /:\left(-\frac{31}{54}\right) \\ y=-24\frac{15}{31} \\ \text{y in I}\\ x =\frac{5}{9} +\frac{20}{27} \cdot -24\frac{15}{31} \\ x=-17\frac{18}{31} \\ L=\{-17\frac{18}{31}/-24\frac{15}{31}\} \end{array} \end{array} \end{array}$