# 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 - Mathematics

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

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

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.6 | Q 1.4 | Page 67