Question

Sa se rezolve sistemul de ecuatii:
ecuatii: 2(x+y)-3xy = 1
5(x+y)+4xy=14​.

Answer 1

Răspuns:

x = 1; y = 1

Explicație pas cu pas:

$\left \{ {{2(x + y) - 3xy = 1} \atop {5(x + y) + 4xy = 14}} \right. \\ \left \{ {{2x + 2y - 3xy = 1} \atop {5x + 5y + 4xy = 14}} \right. \\ \left \{ {{x(2 - 3y) = 1 - 2y} \atop {5x + 5y + 4xy = 14}} \right.\\ \left \{ {{x = \frac{1 - 2y}{2 - 3y}} \atop {5x + 5y + 4xy = 14}} \right.$

$\frac{5(1 - 2y)}{2 - 3y} + 5y + \frac{4y(1 - 2y)}{2 - 3y} = 14 \\ \frac{5 - 10y + 10y - 15 {y}^{2} + 4y - 8 {y}^{2} }{2 - 3y} = 14 \\ \frac{- 23 {y}^{2} + 4y + 5}{2 - 3y} = 14 \\ - 23 {y}^{2} + 4y + 5 = 28 - 42y \\ {y}^{2} - 2y + 1 = 0 \\ (y - 1)^{2} = 1 = > y = 1$

=>

$x = \frac{1 - 2y}{2 - 3y} = \frac{1 - 2}{2 - 3} = > x = 1$