Question

Como determinar a solução dos sistemas aplicando o método da substituição { x+6y=5
{ 2x-3y=5

Answer 1

$\begin{cases}x+6y=5\\ 2x-3y=5\end{cases}\\\\\\[ Isole~~uma~~das~~incognitas~~em ~~uma~~das~~equa{\c c}\~oes, ~~aqui~~vou\\\\ isolar~~x~~na~~1\°:]$



$x+6y=5\to~~x=-6y+5\\\\\\\\[Agora, substitua ~~esse~~valor~~em~~x~~na~~outra~~equa{\c c} \~ao:]\\\\\\ 2x-3y=5\to~~ 2(-6y+5)-3y=5\to~~-12y+10-3y=5\to\\\\ -15y=5-10\to~~-15y=-5~(-1)\to~~15y=5\to ~~y= \dfrac{5}{15} \to\\\\ \boxed{y= \dfrac{1}{3}}\\\\\\\\ [Tendo~~ encontrado~~o ~~valor~~de~~y,~~volte~~na~~1\°~~equa{\c c}\~ao ~~e \\substitua~~em~~y~~afim~~de~~encontrar~~x:]\\\\\\ x=-6y+5\to~~x=-6. \dfrac{1}{3}+5 \to~~ x=\dfrac{-6}{3}+5\to~~x=-2+5\to\\\\ \boxed{x=3}$



$\Large\boxed{\boxed{S=\left\{ 3~;~ \frac{1}{3} \right\}}}$