Question

solve simultenous equations by using replacing and resubstititing method 27/x-2+31/y+3=85 ; 31/x-2+27/y+3=89

Answer 1

Heya..!!!


ler 1/(x - 2) = p

1/(y + 3) = q

now,

27p + 31q = 85------(1)
31p + 27q = 89------(3)

From----(1)and--(2)
Multiply by (31) in --(1) and (27) in ---(2)

we get,

837p + 961q = 2635
837p + 729q = 2403
(-)_____(-)____(-)
————————————
232q = 232

=> q = 232/232

=> q = 1 put in---(1)



we get,


27p + 31(1) = 85

=> 27p = 85 - 31

=> P = 54/27

=> p = 2

=> p = 1/(x - 2) =2

=> 2x - 4 = 1

=> 2x = 5

=> X = 5/2

q = 1/(y + 3) = 1

=> Y + 3 = 1

=> Y = - 2

Answer 2

HELLO DEAR,


let 1/(x - 2) = m
1/(y + 3) = n

27m + 31n = 85---------(1)
31m + 27n = 89----------(2)


subtract--(1) from--(2)

31m + 27n = 89
27m + 31n = 85
(-)_____(-)____(-)
——————————
4m - 4n = 4

=> m - n = 1-------(3)

now,

adding---(1) ---(2)

31m + 27n = 89
27m + 31n = 85
————————
58m + 58n = 174

=> m + n = 3-------(4)

from--(3) &---(4)

we get,

m - n = 1
m + n = 3
—————
2m = 4

=> m = 2 put in--(3)

2 - n = 1

=> n = 1 , m = 2

m = 1/(x - 2) = 2

=> 2x - 4 = 1

=> x = 5/2

n = 1/(y + 3) = 1

=> y + 3 = 1

=> y = -2 , x= 5/2


I HOPE ITS HELP YOU DEAR,
THANKS