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Somit muss der Koeffizient von $x$ null sein: $(4.5+4a)=0\implies a=-\frac{9}{8}$ + +Somit ist unsere Gleichung $0=3c-4.8$. Damit die Lösungsmenge leer ist, darf diese Gleichung nicht erfüllt werden. Also darf $c$ nicht $1.6$ sein. + +$\mathbb{L}_{LGS}=\{\}\Leftrightarrow +a=-\frac{9}{8} \land c \neq \frac{8}{5}$ + +\item 2I+3II:$(8+3p)x=6+3q$ +Damit das LGS singulär ist, darf in dieser Gleichung kein $x$ vorkommen. Somit muss der Koeffizient von $x$ null sein: $8+3p=0\implies p=-\frac{8}{3}$ + +Somit ist unsere Gleichung $0=6+3q$. + +Damit die Lösungsmenge unendlich gross ist, muss diese Gleichung erfüllt werden. $q=-2$ + +Damit die Lösungsmenge leer ist, darf diese Gleichung nicht erfüllt werden. Also darf $q$ nicht $-2$ sein. + + +$|\mathbb{L}_{LGS}|=\infty\Leftrightarrow +p=-\frac{8}{3} \land q=-2$ + + +$\mathbb{L}_{LGS}=\{\}\Leftrightarrow +p=-\frac{8}{3} \land q\neq-2$ + \end{enumerate} \end{document} \ No newline at end of file