b)
[tex]\begin{cases} \frac{1-x}{2} - \frac{y+1}{3} = 0 \ \ \ |\cdot 6 \\ \frac{2x-y}{4} + \frac{y - x}{2} = 7 \ \ \ |\cdot 4 \end{cases} \\\\ \begin{cases} 3 \cdot (1-x) - 2 \cdot (y+1) = 0 \\ 2x- y+2 \cdot (y-x) =28 \end{cases} \\\\ \begin{cases} 3-3x - 2y-2 = 0 \\ 2x- y+ 2y -2x =28 \end{cases} \\\\ \begin{cases} -3x - 2y+1 = 0 \\ y =28 \end{cases} \\\\ \begin{cases} -3x - 2y=-1\\ y =28 \ \ \ |\cdot 2 \end{cases} \\\\ \underline{\begin{cases} -3x - 2y= - 1 \\ 2y =56 \end{cases}} \ \ \ |+[/tex]
[tex]-3x = 55 \ \ \ |:(-3) \\ x = -\frac{55}{3} \\ x = - 18\frac{1}{3} \\\\ y = 28 \\\\ \begin{cases} x = - 18\frac{1}{3} \\ y = 28 \end{cases}[/tex]
Odp. x = - 18¹/₃ i y = 28.
c)
[tex]\begin{cases} \frac{1}{2}x +\frac{1}{3}y = 1 \ \ \ |\cdot 6 \\ - 2x + y = -4 \ \ \ |\cdot (-2) \end{cases} \\\\ \underline{\begin{cases} 3x +2y =6 \\ 4x-2y = 8\end{cases}} \ \ \ |+ \\\\ 7x = 14 \ \ \ |:7 \\ x = 2 \\\\ - 2x + y = -4 \\ - 2 \cdot 2 + y = - 4 \\ - 4 + y = -4 \\ y = -4+4 \\ y = 0 \\\\ \begin{cases} x = 2 \\ y = 0 \end{cases}[/tex]
Odp. x = 2 i y = 0.
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.
