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Solve the Following Systems of Equations: `1/(2x) + 1/(3y) = 2` `1/(3x) + 1/(2y) = 13/6` - CBSE Class 10 - Mathematics

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Question

Solve the following systems of equations:

`1/(2x) + 1/(3y) = 2`

`1/(3x) + 1/(2y) = 13/6`

Solution

Let `1/x = u` and `1/y = v` the given equations become

`u/2 + v/3 = 2`

`=> (3u + 2v)/6 = 2`

=> 3u + 2v = 12 .....(i)

And `u/3 + v/2 = 13/6`

`=> (2u + 3v)/6 = 13/6`

`=> v = 6/2 = 3`

Hence  `x = 1/u = 1/2`  and `y = 1/v = 1/3`

So, the solution of the given system o equation is `x = 1/2, y = 1/3`

  Is there an error in this question or solution?

APPEARS IN

Solution Solve the Following Systems of Equations: `1/(2x) + 1/(3y) = 2` `1/(3x) + 1/(2y) = 13/6` Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method.
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