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

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

1/(3x+y) + 1/(3x-y) = 3/4

1/(2(3x-y)) - 1/(2(3x-y)) = (-1)/8

#### Solution

1/(3x+y) + 1/(3x-y) = 3/4

1/(2(3x-y)) - 1/(2(3x-y)) = (-1)/8

Putting 1/(3x+y) = p  in the given equations, we get

p + q = 3/4 ... (i)

p/2 - q/2 = (-1)/8

p - q = (-1)/4 ... (ii)

Adding (i) and (ii), we get

2p = 3/4 - 1/4

2p = 1/2

p = 1/4

Putting the value in equation (ii), we get

1/4 - q = -1/4

q = 1/4 + 1/4 = 1/2

p = 1/(3x+y) = 1/4

3x + y = 4 ... (iii)

q = 1/(3x-y) = 1/2

3x - y = 2 ... (iv)

Adding equations (iii) and (iv), we get

6x = 6

x = 1 ... (v)

Putting the value in equation (iii), we get

3(1) + y = 4

y = 1

Hence, x = 1 and y = 1

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 1.8 | Page 67