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`

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#### 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

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

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