`{(x^2 - 2xy + 3y^2 = 9 \text{ (1)}),(2x^2 - 18xy + 16y^2 = 0 \text{ (2)}):}`

`(2)` `<=> x^2 - 9xy + 8y^2 = 0`

`<=> x^2 - xy - 8xy + 8y^2 = 0`

`<=> x(x - y) - 8y(x - y) = 0`

`<=> (x - y)(x - 8y) = 0`

`<=>` TH`1`: `x - y = 0 => x = y`

Thay `x = y` vào `(1)` ta có:

`y^2 - 2y^2 + 3y^2 = 9`

`<=> 2y^2 = 9`

`<=> y^2 = (9)/(2)`

`<=> y = \pm (3\sqrt{2})/(2)`

`<=> x = \pm (3\sqrt{2})/(2)`

`<=>` TH`2`: `x - 8y = 0 => x = 8y`

Thay `x = 8y` vào `(1)` ta có:

`(8y)^2 - 2 . (8y) . y + 3y^2 = 9`

`<=> 64y^2 - 16y^2 + 3y^2 = 9`

`<=> 51y^2 = 9`

`<=> y^2 = (3)/(17)`

`<=> y = \pm (\sqrt{51})/(17)`

`<=> x = \pm (8\sqrt{51})/(17)`

Vậy hệ phương trình có nghiệm là $(x; y) \in \left\{ \left(\dfrac{3\sqrt{2}}{2}; \dfrac{3\sqrt{2}}{2}\right), \left(-\dfrac{3\sqrt{2}}{2}; -\dfrac{3\sqrt{2}}{2}\right), \left(\dfrac{8\sqrt{51}}{17}; \dfrac{\sqrt{51}}{17}\right), \left(-\dfrac{8\sqrt{51}}{17}; -\dfrac{\sqrt{51}}{17}\right) \right\}$

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