[Risolto] Aiuto

297)

$x : y = 18 : 6 \quad→\quad x-y = 2$

$6x = 18y$

sistema:

$\left\{\begin{matrix}6x=18y \\ x-y=2\end{matrix}\right\}$

$\left\{\begin{matrix}6x=18y \\ x=2+y\end{matrix}\right\}$

$\left\{\begin{matrix}6(2+y)=18y \\ x=2+y\end{matrix}\right\}$

$\left\{\begin{matrix}12+6y=18y \\ x=2+y\end{matrix}\right\}$

$\left\{\begin{matrix}6y-18y=-12 \\ x=2+y\end{matrix}\right\}$

$\left\{\begin{matrix}-12y=-12 \\ x=2+y\end{matrix}\right\}$

$\left\{\begin{matrix}y=\dfrac{-12}{-12} \\ x=2+y\end{matrix}\right\}$

$\left\{\begin{matrix}y=1 \\ x=2+y\end{matrix}\right\}$

$\left\{\begin{matrix}y=1 \\ x=2+1\end{matrix}\right\}$

$\left\{\begin{matrix}y=1 \\ x=3\end{matrix}\right\}$

 

298)

$\left\{\begin{matrix}x÷y=\dfrac{40}{3}÷5 \\ x-y=5\end{matrix}\right\}$

$\left\{\begin{matrix}5x=\dfrac{40}{3}y \\ x=5+y\end{matrix}\right\}$

$\left\{\begin{matrix}5(5+y)=\dfrac{40}{3}y \\ x=5+y\end{matrix}\right\}$

$\left\{\begin{matrix}25+5y=\dfrac{40}{3}y \\ x=5+y\end{matrix}\right\}$

$\left\{\begin{matrix}5y-\dfrac{40}{3}y=-25 \\ x=5+y\end{matrix}\right\}$

$\left\{\begin{matrix}15y-40y=-75 \\ x=5+y\end{matrix}\right\}$

$\left\{\begin{matrix}-25y=-75 \\ x=5+y\end{matrix}\right\}$

$\left\{\begin{matrix}y=\dfrac{-75}{-25} \\ x=5+y\end{matrix}\right\}$

$\left\{\begin{matrix}y=3 \\ x=5+y\end{matrix}\right\}$

$\left\{\begin{matrix}y=3 \\ x=5+3\end{matrix}\right\}$

$\left\{\begin{matrix}y=3 \\ x=8\end{matrix}\right\}$