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Question
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`
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 `
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