Question

Solve the following systems of equations :
xy/(x + y) = 6/5
xy/(y – x) = 6
where, x + y ≠ 0 and x - y ≠ 0

Answer 1

Step-by-step explanation:

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Answer 2

x = 3/2  ; y = 2

Step-by-step explanation:

Let 1/x = u and 1/y = v

xy/(x + y) = 6/5

5xy = 6x + 6y

Dividing by xy, we get: 5 = 6/y + 6/x

6u + 6v = 5 -------(1)  

xy/(y – x) = 6

 xy = 6y - 6x

Dividing by xy, we get: 1 = 6/x - 6/y

 -6u + 6v = 1 ------------(2)  

Adding 1 & 2, we get: 12v = 6

Therefore v = 1/2

Substituting v in (2), we get: -6u +3 = 1  

Therefore u = 2/3

So u = 1/x = 2/3. Therefore x = 3/2

So v = 1/y = 1/2. Therefore y = 2