Đáp án: `(x;y)=(14/9;10/9)`.
Giải thích các bước giải:
Vì $|x-2y + 2|; |5x-y-4| ≥ 0 ∀ x;y$
$⇒$ $|x-2y+2|+|5x-y-4|=0$ khi:
$|x-2y+2| = |5x-y-4| = 0$
$⇒$ $\left\{\begin{matrix}x-2y+2=0& \\5x-y-4=0& \end{matrix}\right.$
$⇒$ $\left\{\begin{matrix}x-2y=-2& \\5x-y=4& \end{matrix}\right.$
$⇔$ $\left\{\begin{matrix}5x-10y=-10& \\5x-y=4& \end{matrix}\right.$
$⇔$ $\left\{\begin{matrix}5x-10y-(5x-y)=-10-4& \\5x-y=4& \end{matrix}\right.$
$⇔$ $\left\{\begin{matrix}-9y = -14& \\5x-y=4& \end{matrix}\right.$
$⇔$ $\left\{\begin{matrix}y=\dfrac{14}{9}& \\x=\dfrac{10}{9}& \end{matrix}\right.$
Vậy `(x;y)=(14/9;10/9)`.
