Question

Solve for x and y x+y/ху=1 and x-y/xy = 5

Answer 1

(x, y) = (-1/2, 1/3)

Explanation:

Given the simultaneous equation

x+y/ху=1. ...1

x-y/xy = 5 .... 2

From 1; x+y = xy ...3

From 2; x - y = 5xy ...4

Substituting 3 into 4

x - y = 5(x+y)

x - y = 5x + 5y

x - 5x = 5y + y

-4x = 6y

-2x = 3y

x = -3y/2 ... 4

Add 3 and 4

2x = 6xy

2 = 6y

y = 2/6

y = 1/3

x = -3(1/3)/2

x = -1/2

Hence (x, y) = (-1/2, 1/3)