Question

Solve for x and y : 14/x+y+3/x-y=5, 21/x+y-1/x-y=2​

Answer 1

x=4,y=3

Step-by-step explanation:

Let 1/x+y=a and 1/x-y=b

then equation becomes

14a+3b=5---(1)

and 21a-b=2---(2)

multiplying equation (2) by 3 by eliminating method

14a+3b=5

63a-3b=6

________

77a=11

a=1/7

put this value in equation (2)

21(1/7)-b=2

3-b=2

b=1

as 1/x+y=a

then

1/x+y=1/7

x+y=7---(3)

as

1/x-y=b

then

1/x-y=1

x-y=1---(4)

using eliminating method on equation (3) and (4)

x+y=7

x-y=1

_____

2x=8

x=4

put this value in equation (3)

4+y=7

y=3