solve for x and y please tell this very important
Answers
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.
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