Linear equations in two variable pls answer fast its urgent
Answers
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.