Question

Resolva 3x-10y=20 2x+4y=-16

Answer 1

$S=\left\{\begin{matrix}3x-10y=20~~~~(i)\\\\\\2x+4y=-16~~~~(ii) \end{matrix}\right.$


Multiplicando (i) por 2 e (ii) por 5, obteremos o seguinte sistema:


$S'=\left\{\begin{matrix}6x-20y=40~~~~(i)'\\\\\\10x+20y=-80~~~~(ii)' \end{matrix}\right.$


Fazendo (i)' + (ii)' teremos o seguinte:


$S'=\left\{\begin{matrix}6x-20y=40\\\\+\\\\10x+20y=-80\end{matrix}~\Longrightarrow~16x=-40~\Rightarrow~x=-\dfrac{40}{16}~\Rightarrow~x=-\dfrac{5}{2} \right.$


Substituindo x em (i) teremos o seguinte:


$3x-10y=20\\\\\\3\cdot(-\dfrac{5}{2})-10y=20\\\\\\-\dfrac{15}{2}-10y=20~~~~(multiplicando~ambos~os~lados~por~2)\\\\\\-15-20y=40\\\\\\-20y=40+15\\\\\\-20y=55\\\\\\y=-\dfrac{55}{20}\\\\\\y=-\dfrac{11}{4}$


$Solu\c{c}\~ao=\left\{\begin{matrix}x=-\dfrac{5}{2}\\\\\\y=-\dfrac{11}{4} \end{matrix}\right.$