Question

(24/2x+y )-(13 /3x+2y)=2;(26/3x+2y) +(8/2x+y) =3

Answer 1

Answer:

x = 3;. y = 2

Step-by-step explanation:

$\frac{24}{2x + y} - \frac{13}{3x + 2y} = 2 \: \: \: equ \: (1)\\ \frac{26}{3x + 2y} + \frac{8}{2x + y} = 3 \: \: \: \: equ(2)\\ let \\ \: \frac{1}{2x + y} = a \\ \frac{1}{3x + 2y} = b \\ substituting \: a \: and \: b \\ 24a - 13b = 2 \: \: \: equ \: (3)\\ 8a + 26b = 3 \: \: \: \: equ(4) \\ multiply \: equ \: (3) \: with \: 2 \\ 48a - 26b = 4 \: \: \: \: equ \: (5)\\ \\ equ \: (5) - (4) \\ 56a = 7 \\ a = \frac{7}{56} = \frac{1}{8} \\ \\ substituting \: a \: \\ 24 \times \frac{1}{8} - 13b = 2 \\ 3 - 13b = 2 \\ 13b = 1 \\ b = \frac{1}{13} \\ a = \frac{1}{8} = \frac{1}{2x + y} \\ 2x + y = 8 \: \: \: \: equ \: (6)\\ \\ b = \frac{1}{13} = \frac{1}{3x + 2y} \\ 3x + 2y = 13 \: \: \: \: equ(7) \\ multiply \: equ \: (6) \: with \: 2 = 4x + 2y = 16 \\ by \: substraction \: we \: get \\ x = 3 \\ 2x + y = 8 \\ 2(3) + y = 8 \\ 6 + y = 8 \\ y = 2$