Ta có:
$\begin{cases}2x+3y=13\\xy=6\end{cases}$
$⇔\begin{cases}x=\dfrac{13-3y}{2}\\xy=6\end{cases}$
$⇔ \begin{cases}x=\dfrac{13-3y}{2}\\xy=6\end{cases}$
$⇔ \begin{cases}x=\dfrac{13-3y}{2}\\(\dfrac{13-3y}{2})y=6\end{cases}$
$⇔\begin{cases}x=\dfrac{13-3y}{2}\\13y-3y^2=12\end{cases}$
$⇔13y-3y^2=12$
$⇔3y^2-9y-4y+12=0$
$⇔3y(y-3)-4(y-3)=0$
$⇔(y-3)(3y-4)=0$
$⇔$\(\left[ \begin{array}{l}y-3=0\\3y-4=0\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}y=3⇒x=2\\y=\dfrac{4}{3}⇒x=\dfrac{9}{2}\end{array} \right.\)
