Question

reduce the following to linear equations
I) x+y ÷ xy= 2
x-y ÷ xy=6​

Answer 1

Answer:

Step-by-step explanation:

x + y = 2xy

x - y = 6xy

2x = 8xy

→ 2x=8xy → 2 = 8y → (1/4) = y

Put the value of y in x - y = 6xy

→ x - y = 6xy

→ x - (1/4) = 6x(1/4)

→ x - (1/4) = (6x/4)

→ x - (6x/4) = 1/4

→ (4x - 6x)/4 = 1/4

→ - 2x = 1

→ x = - 1/2

x = - 1/2 & y = 1/4

Answer 2

Answer :

x = -1/2 , y = 1/4

Solution :

Here ,

The given equations are ;

(x + y)/xy = 2 --------(1)

(x - y)/xy = 6 --------(2)

Eq-(1) can be rewritten as ;

=> (x + y)/xy = 2

=> x/xy + y/xy = 2

=> 1/y + 1/x = 2 ---------(3)

Eq-(2) can be rewritten as ;

=> (x - y)/xy = 6

=> x/xy - y/xy = 6

=> 1/y - 1/x = 6 ---------(4)

Putting 1/x = a and 1/y = b in eq-(3) and (4) ,

They will be reduced to ;

b + a = 2 ---------(5)

b - a = 6 ----------(6)

Now ,

Adding eq-(5) and (6) , we get ;

=> b + a + b - a = 2 + 6

=> 2b = 8

=> b = 8/2

=> b = 4

=> 1/y = 4

=> y = 1/4

Now ,

Putting b = 4 in eq-(5) , we get ;

=> b + a = 2

=> 4 + a = 2

=> a = 2 - 4

=> a = -2

=> 1/x = -2

=> x = -1/2

Hence ,

x = -1/2 , y = 1/4