Question

Respondam a questão 13 POR FAVOR!! É URGENTE!!!

Answer 1

$\begin{cases}2a-5b=7\\ \dfrac{1}{a+b} = \dfrac{3}{a-b+1} \end{cases}\\\\\\\\ Organizando~~a ~~2\°~~equa\c c\~ao:\\\\\\\dfrac{1}{a+b} = \dfrac{3}{a-b+1}\to~~~multplique~~cruzado:\\\\a-b+1=3a+3b\to~~ a-b-3a-3b=-1\to\\\\ -2a-4b=-1~(-1)\to~~2a+4b=1$



$Ent\~ao~~ agora~~temos:\\\\ \begin{cases}2a-5b=7\\ 2a+4b=1 \end{cases}\\\\Resolvendo~~por~~Adi\c c\~ao:$



$\begin{cases}2a-5b=7\\ 2a+4b=1~(\times-2) \end{cases}\\\\\\ \begin{cases}~~2a-5b=7\\ \underline{-2a-4b=-1} \end{cases}\\ ~~~~~0a-9b=6 \\\\ -9b=6~(-1)\to~~9b=-6\to~~ b=- \dfrac{6}{9} \to~~ \boxed{b=- \dfrac{2}{3} }$



$2a+4b=1\to~~ 2a+4\left( - \dfrac{2}{3} \right)=1\to~~ 2a- \dfrac{8}{3} =1\to~~ 2a=1+ \dfrac{8}{3} \to\\ 2a= \dfrac{11}{3}\to~~a= \dfrac{ \dfrac{11}{3} }{2} \to~~ a=\dfrac{11}{3}\times \dfrac{1}{2}\to~~ \boxed{a=\dfrac{11}{6}}$





$\Large\boxed{\boxed{S=\left\{ \frac{11}{6} ~;~- \frac{2}{3} \right\}}}$