Solve the following pairs of equations by reducing them to a pair of linear equations

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

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

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#### Solution

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

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

Let `1/x = p ` , then the equations changes as below:

`p/2 + q/3 = 2 ` ⇒ 3p + 2q -12 = 0 ... (i)

`p/3 + q/2 = 13/6` ⇒ 2p + 3q -13 = 0 ... (ii)

By cross-multiplication method, we get

`p/(-26-(-36)) = q/(-24-(-39)) = 1/(9-4)`

`p/10 = q/15 = 1/5`

`p/10 = 1/5 `

p = 2 and q = 3

1/x = 2 and 1/y = 3

Hence, `x = 1/2 `

Concept: Equations Reducible to a Pair of Linear Equations in Two Variables

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