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Question
Solve the following pairs of equations by reducing them to a pair of linear equations
`5/(x-1) + 1/y-2 = 2`
`6/(x-1) - 3/(y-2) = 1`
Solution
`5/(x-1) + 1/(y-2) = 2`
`6/(x-1) - 3/(y-2) = 1`
Putting `1/(x-1) = p ` in the given equations, we obtain
5p + q = 2 ... (i)
6p - 3q = 1 ... (ii)
Now, by multiplying equation (i) by 3 we get
15p + 3q = 6 ... (iii)
Now, adding equation (ii) and (iii)
21p = 7
⇒ p = 1/3
Putting this value in equation (ii) we get,
`6×1/(3 - 3q) =1`
⇒ 2-3q = 1
⇒ -3q = 1-2
⇒ -3q = -1
⇒ q = 1/3
Now,
`p = 1/(x-1) = 1/3`
`⇒1/(x-1) = 1/3`
⇒ 3 = x - 1
⇒ x = 4
Also,
`q = 1/(y-2) = 1/3`
`⇒ 1/(y-2) = 1/3`
⇒ 3 = y-2
⇒ y = 5
Hence, x = 4 and y = 5 is the solution
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