Question

5/2x+2/3y=7, 3/x+2/y=12​

Answer 1

Answer:

x = 1/2 y = 1/3

Step-by-step explanation:

$\frac{5}{2x} + \frac{2}{3y} = 7 \: equ \: (1) \\ \frac{3}{x} + \frac{2}{y} = 12 \: equ \: (2) \\ multiply \: equ \: (1) \: with \: 6 \: and \: equ \: (2) \: with \: 2 \\ \frac{15}{x} + \frac{4}{y} = 42 \: \: equ \: (3) \\ \frac{6}{x} + \frac{4}{y} = 24 \: equ \: (4) \\ subtract \: equ \: (3) - equ(4) \\ \frac{15}{x} - \frac{6}{x} = 42 - 24 \\ \frac{15 - 6}{x} = 18 \\ \frac{9}{x} = 18 \\ 18x = 9 \\ x = \frac{9}{18} \\ x = \frac{1}{2} \\ \\ substitute \: x = \frac{1}{2} \: in \: equ \: (2) \\ \frac{3}{ \frac{1}{2} } + \frac{2}{y} = 12 \\ 6 + \frac{2}{y} = 12 \\ \frac{2}{y} = 12 - 6 \\ \frac{2}{y} = 6 \\ 2 = 6y \\ y = \frac{2}{6} \\ y = \frac{1}{3}$

x = 1/2 y = 1/3

verification

$\frac{5}{2 \times \frac{1}{2} } + \frac{2}{3 \times \frac{1}{3} } \\ = \frac{5}{1} + \frac{2}{1} \\ = 5 + 2 \\ = 7$

Hope you get your answer