Question

Solve 2/x+3/y=13,5/x+7/y=31

Answer 1

Answer:

x = 1/2

y = 1/3

Step-by-step explanation:

let 1/x = a and 1/y = b

$2a + 3b = 13 \: \: \: \: equ \: (1) \\ 5a + 7b = 31 \: \: \: \: equ \: (2) \\ multipy \: equ \: (1 ) \: with \: 5 \: and \: equ \: (2) \: with \: 2 \\ 10a + 15b = 65 \: \: \: \: equ \: (3) \\ 10a + 14b = 62 \: \: \: equ \: (4) \\ \\ subtract \: equ \: (3) - (4) \\ b = 3$

substitute b = 3 in equ (1)

2a + 3b = 13

2a + 3(3) = 13

2a + 9 = 13

2a = 13 - 9

2a = 4

a = 4/2 = 2

a = 2 = 1/x x = 1/2

b = 3 = 1/y y = 1/3

verification

$= \frac{2}{ \frac{1}{2} } + \frac{3}{ \frac{1}{3} } \\ = 2(2) + 3(3) \\ = 4 + 9 \\ = 13 \\ \\ \frac{5}{ \frac{1}{2} } + \frac{7}{ \frac{1}{3} } \\ = 5(2) + 7(3) \\ = 10 + 21 \\ = 31$

hope you get your answer