Question

Solve the following systems of equations:
6/(x + y) = 7/(x – y) + 3
1/2(x + y) = 1/3(x – y)
where, x + y ≠ 0 and x - y ≠ 0

Answer 1

x = -5/4 ;  y  = -1/4

Step-by-step explanation:

Let 1/(x +y) = u and 1/(x-y) = v

 6/(x + y) = 7/(x – y) + 3

 6u - 7v = 3 ------------(1)  

 1/2(x + y) = 1/3(x – y)

 1/2(u) = 1/3(v)

 3u = 2v

 3u - 2v = 0 ------------(2)

(2)*2, we get: 6u - 4v = 0 -----(3)

Subtracting 3 from 1, we get: -3v = 3

Therefore v = -1

Substituting in (2), we get: 3u +2 = 0

Therefore u = -2/3

So u = 1/(x +y) = -2/3.

 x + y = -3/2  

 2x + 2y = -3 -----(4)

So v = 1/(x-y) = -1.

 x - y = -1 -----(5)

Adding (4) and 2(5), we get: 4x = -5

Therefore x = -5/4

Substituting in (5), we get -5/4 - y = -1

-y = -1 + 5/4

 y = 1 - 5/4

 y  = -1/4