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