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Question
Solve the following systems of equations:
2(3u − ν) = 5uν
2(u + 3ν) = 5uν
Solution
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
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