Question

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Answer 1

Answer:

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Answer 2

5/(x + y) - 2/(x - y) = -1 ------------eq1

15/(x + y) - 7/(x - y) = 10 ---------eq2

Let,

1/(x + y) = a

1/(x - y) = b

now the equations will look like :-

5a - 2b = -1 ---------eq2

15a + 7b = 10-------eq3

solve equations 2 and 3

make coefficient of equation 2 same by multiplying it by 3 and equation 3 by 1

5a - 2b = -1 ----- × 3

15a + 7b = 10 ----- × 1

15a - 6b = -3

15a + 7b = 10

- - -

----------------------

0 - 13b = -13

-13b = -13

b = 1

put this in eq 1 or 2 to find a

eq1

15a - 6b = -3

15a - 6b = -315a - 6(1) = -3

15a - 6b = -315a - 6(1) = -315a = 6 - 3

15a - 6b = -315a - 6(1) = -315a = 6 - 315a = 3

a = 1/5

Now,

1/(x + y) = 1/5 = x + y = 5-----eq4

1/(x - y) = 1 = x - y = 1 -------eq5

x + y = 5

x - y = 1

-------------

2x - 0 = 6

2x = 6

x = 3

put this in eq 4 or 5 to get y

x + y = 5

y = 5 - x

y = 5 - 3

y = 2