Răspuns:
x = -1; y = -1
Explicație pas cu pas:
x ≠ -3 ; y ≠ -2
[tex]\frac{2}{x + 3} + \frac{3}{y + 2} = 4 \\ \frac{3}{x + 3} + \frac{2}{y + 2} = \frac{7}{2}[/tex]
[tex]2(y + 2) + 3(x + 3) = 4(x + 3)(y + 2) \\ 2 \times 3(y + 2) + 2 \times 2(x + 3) =7(x + 3)(y + 2)[/tex]
[tex]2y + 4 + 3x + 9 = 4xy + 8x + 12y + 24 \\ 6y + 12 + 4x + 12 + 7xy + 14x + 21y + 42[/tex]
[tex]4xy + 5x + 10y + 11 = 0\\7xy + 10x + 15y + 18 = 0[/tex]
[tex]x(4y + 5) = - 10y - 11 = > x = \frac{ - 10y - 11}{4y + 5} [/tex]
[tex]x(7y + 10) + 15y + 18 = 0 = > \frac{ - 10y - 11}{4y + 5} \times (7y + 10) + 15y + 18 = 0[/tex]
[tex]-(10y + 11)(7y + 10) + (15y + 18)(4y + 5) = 0 = > - 70 {y}^{2} - 100y - 77y - 110 + 60y^{2} + 75y + 72y + 90 = 0 = > - 10 {y}^{2} - 30y - 20 = 0[/tex]
[tex]{y}^{2} + 3y + 2 = 0 \\ (y + 1)(y + 2) = 0 = > y = - 1 [/tex]
[tex]x = \frac{ - 10( - 1) - 11}{4( - 1) + 5} = \frac{10 - 11}{ - 4 + 5} = \frac{ - 1}{1} = - 1 [/tex]
[tex] = > x = - 1[/tex]
