Question

Solve the following systems of equations:
2(3u - v) = 5uv
2(u + 3v) = 5uv

Answer 1

Answer:

Step-by-step explanation:

Answer 2

u = 2  ; v = 1

Step-by-step explanation:

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

2(3u - v) = 5uv

6u - 2v = 5uv

Dividing by uv, we get: 6/v - 2/u = 5

-2x +6y = 5-------(1)  

2(u + 3v) = 5uv

2u + 6v = 5uv  

Dividing by uv, we get: 2/v + 6/u = 5

 6x + 2y = 5 ------------(2)  

Adding (1)*3 & 2, we get: 20y = 20

Therefore y = 1

Substituting y in (1), we get: -2x + 6 = 5  

Therefore x = 1/2

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

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