1. Tìm các cặp số nguyên x.y thỏa mãn: 3xy+2x-5y=6

<p>1)&nbsp;</p><p>$\begin{aligned} &amp; 3 x y+2 x-5 y=6 \Rightarrow x(3 y+2)-5 y=6 \Rightarrow 3 x(3 y+2)-15 y=18 \\ &amp; \Rightarrow 3 x(3 y+2)-15 y-10=18-10 \Rightarrow 3 x(3 y+2)-5(3 y+2)=8 \\ &amp; \Rightarrow(3 x-5)(3 y+2)=8 \\ &amp; \Rightarrow 3 y+2 \in U(8)=\{\pm 1 ; \pm 2 ; ; \pm 4 ; \pm 8\} \end{aligned}$</p><p>Mà&nbsp;$3 y+2$&nbsp;là số chia cho 3 dư&nbsp;$2 \Rightarrow 3 y+2 \in\{-1 ; 2 ;-4 ; 8\}$.</p><p>Ta có bảng sau:</p><p><img src="https://static.questionai.vn/resource/qaiseoimg/202501/3-y2-4-1-2-8-3-x5-2-8-4-1-y-2-1-0-2-x-1-1-3-2-tVZ0xhQ9y902.jpg" alt=" 3 y+2 & -4 & -1 & 2 & 8 3 x-5 & -2 & -8 & 4 & 1 y & -2 & -1 & 0 & 2 x & 1 & -1 & 3 & 2 "></p><p>Vậy&nbsp;$(x ; y) \in\{(1 ;-2),(-1 ;-1),(3 ; 0),(2 ; 2)\}$.</p><p><br/></p>