\(3xy+x+15y-44=0\)

\(3y\left(x+5\right)+\left(x+5\right)-49=0\)

\(\left(x+5\right)\left(3y+1\right)=49\)

Vì x;y là số nguyên \(\Rightarrow\hept{\begin{cases}x+5\in Z\\3y+1\in Z\end{cases}}\)

Có \(\left(x+5\right)\left(3y+1\right)=49\)

\(\Rightarrow\left(x+5\right)\left(3y+1\right)\in\text{Ư}\left(49\right)=\left\{\pm1;\pm7;\pm49\right\}\)

b tự lập bảng nhé~

2x\(^2\)+y\(^2\)+3xy+3x+2y+2=0

\(\Leftrightarrow\)16x\(^2\)+8y\(^2\)+24xy+24x+16y+16=0

\(\Leftrightarrow\)(4x)\(^2\)+24x(y+1)+8y\(^2\)+16y+16=0

\(\Leftrightarrow\)(4x)\(^2\)+24x(y+1)+[3(y+1)]\(^2\)-[3(y+1)]\(^2\)+8y\(^2\)+16y+16=0

\(\Leftrightarrow\)(4x+3y+3)\(^2\)-9y\(^2\)-18y-9+8y\(^2\)16y+16=0

\(\Leftrightarrow\)(4x+3y+3)\(^2\)-y\(^2\)-2y-1+8=0

\(\Leftrightarrow\)(4x+3y+3)\(^2\)- (y+1)\(^2\)= -8

\(\Leftrightarrow\)(y+1+4x+3y+3) (y+1-4x-3y-3)=8

\(\Leftrightarrow\)4(x+y+4) (-4-2y-2)=8

\(\Leftrightarrow\)(x+y+4) (2x+y+11)= -1

\(\Leftrightarrow\){x+y+4= -1

      {2x+y+1=1

\(\Rightarrow\)x=2 và y= -4

{x+y+4= 1

{2x+y+1= -1

\(\Rightarrow\)x=-2 và y=2

vậy nghiệm (x,y)=(-2;4) (-2;2)

tải Qanda về mà hỏi