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प्रश्न
Solve for x and y:
`5/(x+y) - 2/(x−y) = -1, 15/(x+y) - 7/(x−y) = 10`
उत्तर
The given equations are
`5/(x+y) - 2/(x−y)= -1` ……(i)
`15/(x+y) - 7/(x−y) = 10` ……(ii)
Substituting `1/(x+y) = u and 1/(x−y) = v` in (i) and (ii), we get
5u – 2v = -1 ……..(iii)
15u + 7v = 10 …….(iv)
Multiplying (iii) by 3 and subtracting it from (iv), we get
7v + 6v = 10 + 3
⇒13v = 13
⇒v = 1
`⇒x – y = 1 (∵1/(x−y)=v)` …..(v)
Now, substituting v = 1 in (iii), we get
5u – 2 = -1
⇒5u = 1
`⇒u = 1/5`
x + y = 5 …….(vi)
Adding (v) and (vi), we get
2x = 6 ⇒ x = 3
Substituting x = 3 in (vi), we have
3 + y = 5 ⇒ y = 5 – 3 = 2
Hence, x = 3 and y = 2.
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