d)
[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)=(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-2xy+y+2xy = 9 \end{cases} \\\\ \begin{cases}9x^2 - 6x + 1 -4y^2-12y -9-9x^2+4y^2-1=0 \\ 2x+y= 9 \end{cases} \\\\ \begin{cases} - 6x -12y -9=0 \\ 2x+y= 9 \ \ \ |\cdot 3 \end{cases} \\\\ \underline{\begin{cases} - 6x -12y=9 \\ 6x+3y= 27 \end{cases}} \ \ \ | +[/tex]
[tex]- 9y = 36 \ \ \ |:(-9) \\ y = - 4 \\\\ 2x +y = 9 \\ 2x - 4= 9 \\ 2x = 9 + 4 \\ 2x = 13 \ \ \ |:2 \\ x = \frac{13}{2} \\ x = 6\frac{1}{2} \\\\ \begin{cases} x =6\frac{1}{2} \\ y = - 4 \end{cases}[/tex]
Odp. x = 6¹/₂ i y = - 4.
