Question

please solve this question

Answer 1

Given equations,

10 / (x + y) + 2 / (x - y) = 4

15 / (x - y) + 5 / (x - y) = 2

Let, 1 / (x + y) = m and 1 / (x - y)= n

We get the equations,

10m + 2n = 4 --------(1)

15m + 5n = 2 --------(2)

From (1) × 5 and (2) × 2 , We get

50m + 10n = 20

30m + 10n = 4 ___ [ By Subtracting ]
(-) __(-) ___(-)
---------------------
20m = 16

→ m = 16/20

→ m = 4/5

Putting m = 4/5 in (1) , We get

10 × (4/5) + 2n = 4

2×4 + 2n = 4

→ 8 + 2n = 4

→ 2n = 4 - 8

→ n = - 4/2

→ n = - 2

Now,

As consider, We have

1 / (x + y) = m

→ 1 / (x + y) = 4/5

→ x + y = 5/4 --------(3)

and

1 / (x - y) = n

→ 1 / (x - y) = 2

→ x - y = 1/2 --------(4)

Adding (3) and (4), We get

x + y + x - y = 5/4 + 1/2

→ 2x = (5 - 2) / 4

→ 2x = 3/4

→ x = 3/8

Putting in (3), We get

3/8 + y = 5/4

→ y = 5/4 - 3/8

→ y = (10 - 3) / 8

→ y = 7/8

Hence,

$\boxed{ \mathbf{x \: = \frac{ 3}{8} } \: \: \: \: and\: \: \: \: \mathbf{y = \frac{7}{8} }\:}$