Question

Seja o sistema

{12x+3y=4
8x-4y=2, encontre o valor de x y

Answer 1

$\begin{cases}12x + 3y = 4\\ 8x - 4y = 2\end{cases}\\\\\\\\ 8x - 4y = 2\to~~ 8x=4y+2\to~~x= \dfrac{4y+2}{8} \to~~ x= \dfrac{2y+1}{4} \\\\\\\\ 12x + 3y = 4\to~~12\left( \dfrac{2y+1}{4}\right) + 3y = 4\to~~\dfrac{24y+12}{4}+ 3y = 4\to\\\\\\ 6y+3+3y=4\to~~ 6y+3y=4-3\to~~9y=1\to~~\boxed{y= \frac{1}{9} }$




$x= \dfrac{2y+1}{4} \to~~x= \dfrac{2\left( \dfrac{1}{9}\right)+1}{4} \to~~ x= \dfrac{\dfrac{2}{9}+1}{4} \to~~ x= \dfrac{\dfrac{2+9}{9}}{4} \to\\\\\\ x= \dfrac{\dfrac{11}{9}}{4} \to~~ x=\dfrac{11}{9}\times\dfrac{1}{4}\to~~\boxed{x=\dfrac{11}{36}}\\\\\\\\\\ \large\boxed{\boxed{S=\left\{\dfrac{11}{36}~;~\dfrac{1}{9} \right\}}}$