Question

solve x+y/xy=6,x-y/xy=2 pair of equation reducing them to a pair of linear equations​

Answer 1

Answer :-

Required solution is x = 1 / 2 and y = 1 / 4.

Explanation :-

Given pair of equations :-

→ (x + y) / xy = 6

→ (x - y) / xy = 2

(x + y) / xy = 6

⇒ ( x / xy ) + ( y / xy ) = 6

⇒ ( 1 / y ) + ( 1 / x ) = 6

(x - y) / xy = 2

⇒ ( x / xy ) - ( y / xy ) = 2

⇒ ( 1 / y ) - ( 1 / x ) = 2

On simplifying we get,

→ ( 1 / y ) + ( 1 / x ) = 6

→ ( 1 / y ) - ( 1 / x ) = 2

Sustituting a = 1 / y and b = 1 / x we get,

→ a + b = 6 --- eq(1)

→ a - b = 2 --- eq(2)

Adding eq(1) and eq(2)

⇒ a + b + ( a - b ) = 6 + 2

⇒ a + b + a - b = 8

⇒ 2a = 8

⇒ a = 8 / 2

⇒ a = 4

But, a = 1 / y

⇒ 4 = 1 / y

⇒ y = 1 / 4

Substuting a = 4 in eq(1)

⇒ a + b = 6

⇒ 4 + b = 6

⇒ b = 6 - 4

⇒ b = 2

But, b = 1 / x

⇒ 2 = 1 / x

⇒ x = 1 / 2

Hence, the required solution is x = 1 / 2 and y = 1 / 4.