Question

solve for x and y please tell this very important​

Answer 1

EXPLANATION.

⇒ 10/(x + y) + 2/(x - y) = 4. - - - - - (1).

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

As we know that,

Let, we assume that,

⇒ 1/(x + y) = a.

⇒ 1/(x - y) = b.

We can write equation as,

⇒ 10a + 2b = 4. - - - - - (1).

⇒ 15a - 5b = - 2. - - - - - (2).

Multiply equation (1) by 5.

Multiply equation (2) by 2.

We get,

⇒ 10a + 2b = 4. - - - - - (1). x 5.

⇒ 15a - 5b = - 2. - - - - - (2). x 2.

We get,

⇒ 50a + 10b = 20. - - - - - (3).

⇒ 30a - 10b = - 4. - - - - - (4).

Adding equation (3) & (4), we get.

⇒ 80a = 16.

⇒ a = 16/80.

⇒ a = 1/5.

Put the value of a = 1/5 in the equation (1), we get.

⇒ 10a + 2b = 4.

⇒ 10x (1/5) + 2b = 4.

⇒ 2 + 2b = 4.

⇒ 2b = 4 - 2.

⇒ 2b = 2.

⇒ b = 1.

Value of a = 1/5 and b = 1.

Put the value of a and b in the original equation, we get.

⇒ 1/x + y = a.

⇒ 1/x + y = 1/5.

⇒ x + y = 5. - - - - - (5).

⇒ 1/x - y = b.

⇒ 1/x - y = 1.

⇒ x - y = 1. - - - - - (6).

From equation (5) & (6), we get.

⇒ x + y = 5. - - - - - (5).

⇒ x - y = 1. - - - - - (6).

Adding equation (5) & (6), we get.

⇒ 2x = 6.

⇒ x = 3.

Put the value of x = 3 in the equation (5), we get.

⇒ x + y = 5.

⇒ 3 + y = 5.

⇒ y = 5 - 3.

⇒ y = 2.

Values of x = 3   and  y = 2.

Answer 2

plz mark me as brainlist