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प्रश्न
Solve the following systems of equations:
`5/(x + y) - 2/(x - y) = -1`
`15/(x + y) + 7/(x - y) = 10`
उत्तर
Let `1/(x + y) = u` and `1/(x - y) = v`Then, the given system off equations becomes
5u - 2v = -1 .....(i)
15u + 7v = 10 .....(ii)
Multiplying equation (i) by 7, and equation (ii) by 2, we get
35u - 14v = -7 ....(iii)
30u + 14v = 20 ....(iv)
Adding equation (iii) and equation (iv), we get
`=> 35u + 360u = -7 + 20`
=> 65u = 13
`=> u = 13/65 = 1/5`
Putting `u = 1/5` in equation (i) we get
`5 xx1/5 - 2v = -1`
=> 1 - 2v = -1
`=> -2v = -1-1`
=> -2v = -2
`=> v = (-2)/(-2) = 1`
Now `u = 1/(x + y)`
`=> 1/(x + y) = 1/5`
=> x + y = 5 ....(v)
and `v = 1/(x - y) =1`
=> x - y = 1 ....(vi)
Adding equation (v) and equation (vi), we get
2x = 5 + 1
=> 2x = 6
`=> x = 6/2 = 3`
Putting x = 3 in equation (v), we get
3 + y = 5
`=> y = 5 - 3 = 2`
Hence, solution of the given system of equation is x = 3, y = 2.
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