Question

solve the pair of equation x+y/xy=2, x-y/xy=6.

Answer 1

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

Given :

pair of equations

(x +y) / xy = 2,

(x -y) / xy = 6.

To find :

solve the given pair of equations

x+y/xy=2,

x-y/xy=6.

Solution :

(x +y) / xy = 2 →(1)

(x -y) / xy = 6 → (2)

from equation (1)

multiplying with xy both the sides

( x + y) = 2 xy →(3)

from equation (2)

multiplying with xy both the sides.

( x - y) = 6 xy → (4)

considering equation (3) and (4)

adding equation (3) and (4)

x +y = 2xy

x - y = 6 xy

__________

2x + 0 = 8xy

2x= 8 xy

y = 2x / 8x

y = 1/4

substituting value of y in equation (3)

x + y = 2 xy

x + 1/4 = 2 (1/4) x

v 4 X+ 1 = 4 (1/2) X

4X + 1 = 2X

4X - 2X = -1

2X = - 1

X = ( -1/2)

Hence X = -1/2 , Y = 1/4.