Question

Solve the following systems of equations:

2(3u − ν) = 5uν
2(u + 3ν) = 5uν

Answer 1

The system of the given equation is

2(3u − ν) = 5uν

=> 6u - 2v = 5uv ....(i)

And 2(u + 3v) = 5uv

=> 2u + 6v = 5uv .....(ii)

Multiplying equation (i) by 3 and equation (ii) by 1, we get

18u - 6v = 15uv ...(iii)

2u + 6v = 5uv ...(iv)

Adding equation (iii) and equation (iv), we get

18u + 2u = 156uv + 5uv

=> 20u = 20uv

`=> (20u)/(20u)= v`

=> v = 1

Putting v = 1in equation (i), we get

6u - 2 x 1 = 5u x 1

=> 6u - 2 = 5u

=> 6u - 5u = 2

=> u = 2

Hence, solution of the given system of equation is u = 2, v=- 1