# 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/(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

Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.6 | Q 1.1 | Page 67