[tex]\begin{cases}(3x-1)^2- (2y+3)^2= (3x-2y)(3x+2y)+1\\2x(1-y)+y(1+2x)=9\end{cases}\\\\\begin{cases}9x^2-6x+1-4y^2-12y-9=9x^2-4y^2+1\\2x-2xy+y+2xy=9\end{cases}\\\\\begin{cases}-6x+1-12y-9=1\\ 2x+y=9\end{cases}}\\\\\begin{cases}-6x-12y=9\qquad|:3\\ 2x+y=9\end{cases}\\\\\underline{\begin{cases}-2x-4y=3\\\ \ 2x+y=9\end{cases}}\\{}\qquad-3y=12\qquad|:(-3)\\{}\qquad\quad y = -4\\\\2x+(-4)=9\\2x=13\\x=6{,}5[/tex]
[tex]\begin{cases}x=6{,}5\\y=-4\end{cases}[/tex]
