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Solve the Following Systems of Equations: `(7x - 2y)/"Xy" = 5` `(8x + 7y)/"Xy" = 15` - CBSE Class 10 - Mathematics

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Question

Solve the following systems of equations:

`(7x - 2y)/"xy" = 5`

`(8x + 7y)/"xy" = 15`

Solution

`(7x - 2y)/"xy" = 5`

`=> 7/y - 2/x = 5` .....(1)

`(8x + 7y)/(xy) = 15`

`=> 8/y + 7/x = 15` ..........(2)

Let `1/x = p and 1/y = q`

The given equations reduce to:

-2p + 7q = 5

=> -2p + 7q - 5 = 0 ...(3)

7p + 8q = 15

=> 7p + 8q - 15 = 0 ....(4)

Using cross multiplication method, we obtain:

`p/(-105-(-40)) = q/(-35-30) = 1/(-16-49)`

`p/(-65) = 1/(-65), q/(-65) = 1/(-65)`

p = 1, q= 1

`p = 1/x = 1, q= 1/y =1`

x = 1 , y = 1

  Is there an error in this question or solution?

APPEARS IN

Solution Solve the Following Systems of Equations: `(7x - 2y)/"Xy" = 5` `(8x + 7y)/"Xy" = 15` Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method.
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