Question

Linear equations in two variable pls answer fast its urgent​

Answer 1

EXPLANATION.

⇒ 1/(3x + y) + 1/(3x - y) = 3/4. - - - - - (1).

⇒ 1/2(3x + y) - 1/2(3x - y) = -1/8. - - - - - (2).

As we know that,

Let we assume that,

⇒ 1/(3x + y) = a.

⇒ 1/(3x - y) = b.

Equation can be written as,

⇒ a + b = 3/4. - - - - - (3).

⇒ a/2 - b/2 = -1/8. - - - - - (4).

⇒ a - b = -1/4. - - - - - (4).

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

Adding both the equations, we get.

⇒ a + b = 3/4. - - - - - (3).

⇒ a - b = -1/4. - - - - - (4).

We get,

⇒ 2a = 3/4 - 1/4.

⇒ 2a = 2/4.

⇒ 2a = 1/2.

⇒ a = 1/4.

Put the value of a = 1/4 in equation (3), we get.

⇒ 1/4 + b = 3/4.

⇒ b = 3/4 - 1/4.

⇒ b = 2/4.

⇒ b = 1/2.

Compare the equation with real equation, we get.

⇒ 1/(3x + y) = a.

⇒ 1/(3x + y) = 1/4.

⇒ 3x + y = 4. - - - - - (5).

⇒ 1/(3x - y) = b.

⇒ 1/(3x - y) = 1/2.

⇒ 3x - y = 2. - - - - - (6).

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

Adding both the equations, we get.

⇒ 3x + y = 4.

⇒ 3x - y = 2.

We get,

⇒ 6x = 6.

⇒ x = 1.

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

⇒ 3(1) + y = 4.

⇒ 3 + y = 4.

⇒ y = 4 - 3.

⇒ y = 1.

Value of x = 1 & y = 1.