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Question
Solve the following systems of equations:
`3/x - 1/y = -9`
`2/x + 3/y = 5`
Solution
Let 1/x = u and 1/y Then, the given system of equations becomes
3u - v = -9 ....(i)
2u + 3v = = 5 ....(ii)
Multiplying equation (i) by 3 an equation (ii) by 1, we get
9u - 3v = -27 ....(iii)
2u + 34v = 5 ...(iv)
Adding equation (i) and equation (ii), we get
9u + 2u - 3v + 3v = -27 + 5
=> 11u = -22
`=> u = (-22)/11 = -2`
Putting u = -2 in equation (iv), we get
`2 xx (-2) + 3v = 5`
`=> -4 + 3v = 5`
=> 3v = 5 + 4
=> v = 9/3 = 3
Hence `x = 1/u = 1/(-2) = (-1)/2` and `y = 1/v = 1/3`
So, the solution of the given system of equation is `x = (-1)/2 , y = 1/3`
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