Question

x+y=5 fraçao 5/6 e x-y= 1/6 fraçao!

Answer 1

$x+y=5\frac{5}{6}=\frac{35}{6}\\ \\ x-y=\frac{1}{6}\\ \\ Adicionando \ as \ equacoes:\\ \\ 2x=\frac{36}{6}\\ 2x=6\\ x=3$

Substituindo o valor de x:

$3+y=\frac{5}{6}\\ 18+6y=5\\ 6y=5-18\\ 6y=-13\\ y=-\frac{13}{6}$

Resposta:  $S=\{3,-\frac{13}{6}\}$

Answer 2

$\begin{cases}x+y= \dfrac{5}{6} \\\\ x-y= \dfrac{1}{6} \end{cases}\\\\\\\\ x+y= \dfrac{5}{6} \to~~ x=-y+ \dfrac{5}{6} \\\\\\\\ x-y= \dfrac{1}{6}\to~~ -y+ \dfrac{5}{6} -y= \dfrac{1}{6}\to~mmc=6\to~ -6y+5-6y=1\to\\\\ -6y-6y=1-5\to~~-12y=-4~(-1)\to~~12y=4\to~~y= \dfrac{4}{12} \to\\\\ \large\boxed{y= \frac{1}{3} }$



$x=-y+ \dfrac{5}{6} \to~~ x=- \dfrac{1}{3} + \dfrac{5}{6} \to~~mmc=6\to~~ 6x=-2+5\to\\\\ 6x=3\to~~ x= \dfrac{3}{6} \to~~ \large\boxed{x= \frac{1}{2} }\\\\\\\\\\\\ \Large\boxed{\boxed{S=\left\{ \frac{1}{2} ~;~ \frac{1}{3} \right\}}}$