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प्रश्न
Solve the following pair of equations:
`1/(2x) - 1/y = -1, 1/x + 1/(2y) = 8, x, y ≠ 0`
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उत्तर
Given pair of linear equations are
`1/(2x) - 1/y` = – 1 ......(i)
And `1/x + 1/(2y)` = 8, x, y ≠ 0 ......(ii)
Let u = `1/x` and v = `1/y`,
Then the above equations become
`u/2 - v` = – 1
⇒ u – 2v = – 2 ....(iii)
And `u + v/2` = 8
⇒ 2u + v = 16 .....(iv)
On multiplying equation (iv) by 2 and then adding with equation (iii), we get
4u + 2v = 32
u – 2v = – 2
5u = 30
⇒ u = 6
Now, put the value of u in equation (iv), we get
2 × 6 + v = 16
⇒ v = 16 – 12 = 4
⇒ v = 4
∴ x = `1/u = 1/6`
And y = `1/v = 1/4`
Hence the required values of x and y are `1/6` and `1/4`, respectively.
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