Question

Calcule o valor das letras nas proporções:


$\left \{ {{x+y=27} \atop {\frac{x}{y} = \frac{4}{5}}} \right. \\ \\ \\ \left \{ {x.y=135} \atop { \frac{x}{3} = \frac{y}{5} }} \right.$

Answer 1

Olá, Davi.

$a)\ \begin{cases}x+y=27\,\,(\times5)\\\frac x y=\frac45\end{cases}\Rightarrow\begin{cases}5x+5y=135\\5x=4y\end{cases}\Rightarrow4y+5y=135\Rightarrow\\\\\\9y=135\Rightarrow\boxed{y=15}\Rightarrow5x=4\cdot15=60\Rightarrow\boxed{x=12}$


$b)\ \begin{cases}xy=135\\\frac x 3=\frac y 5\end{cases}\Rightarrow\begin{cases}xy=135\\x=\frac35y\,\,(\times y)\end{cases}\Rightarrow\begin{cases}xy=135\\xy=\frac35y^2\end{cases}\Rightarrow\frac35y^2=135\Rightarrow\\\\\\y^2=\frac53\cdot135=5\cdot45=225\Rightarrow y=\pm\sqrt{225}\Rightarrow\boxed{y_1=-15\ ou\ y_2=15}\\\\ Se\ y_1=-15\Rightarrow x_1=\frac35\cdot(-15)\Rightarrow\boxed{x_1=-9}\\\\ Se\ y_2=15\Rightarrow x_2=\frac35\cdot15\Rightarrow\boxed{x_2=9}$

$\therefore\boxed{S=\{(-9;-15),(9;15)\}}$