5x² + 4y² - 4xy = 6x - 4y - 2

5x² +4y² - 4xy - 6x - 4y - 2 = 0

(x² -4xy + 4y²) - 2x + 4y +4x² - 4x + 2 = 0

(x - 2y)² - 2(x - 2y).1 + 1² +(4x² - 4x + 1²) = 0

(x - 2y - 1)² + (2x - 1)² = 0

⇒\(\left\{{}\begin{matrix}x-2y-1=0\\2x-1=0\end{matrix}\right.\)

⇒\(\left\{{}\begin{matrix}x-2y-1=0\Rightarrow\frac{1}{2}-2y-1=0\Rightarrow\frac{-1}{2}-2y=0\Rightarrow y=\frac{-1}{4}\\x=\frac{1}{2}\end{matrix}\right.\)

Vậy \(\left\{{}\begin{matrix}x=\frac{1}{2}\\y=\frac{-1}{4}\end{matrix}\right.\)