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प्रश्न
Solve the following pairs of equations by reducing them to a pair of linear equations
`(7x-2y)/(xy) = 5`
`(8x + 7y)/(xy) = 15`
उत्तर
`(7x-2y)/(xy) = 5`
`⇒ (7x)/(xy) - (2y)/(xy) = 5`
`⇒ 7/y - 2/x = 5 ... (i)`
`(8x+7y)/(xy) = 15`
`⇒ (8x)/(xy) + (7y)/(xy) = 15`
`⇒ 8/y + 7/x = 15 ... (ii)`
Putting `1/x = p ` in (i) and (ii) we get,
7q - 2p = 5 ... (iii)
8q + 7p = 15 ... (iv)
Multiplying equation (iii) by 7 and multiplying equation (iv) by 2 we get,
49q - 14p = 35 ... (v)
16q + 14p = 30 ... (vi)
Now, adding equation (v) and (vi) we get,
49q - 14p + 16q + 14p = 35 + 30
⇒ 65q = 65
⇒ q = 1
Putting the value of q in equation (iv)
8 + 7p = 15
⇒ 7p = 7
⇒ p = 1
Now,
p = 1/x = 1
⇒ 1/x = 1
⇒ x = 1
also, q = 1 = 1/y
⇒ 1/y = 1
⇒ y = 1
Hence, x =1 and y = 1 is the solution
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