# Solve the following pairs of equations by reducing them to a pair of linear equations 6x + 3y = 6xy, 2x + 4y = 5xy - Mathematics

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

6x + 3y = 6xy

2x + 4y = 5xy

#### Solution

6x + 3y = 6xy

⇒ (6x)/(xy) + (3y)/(xy) = 6

⇒ 6/y + 3/x = 6 ... (i)

2x + 4y = 5xy

⇒ (2x)/(xy) + (4y)/(xy) = 5

⇒ 2/y + 4/x = 5 ... (ii)

Putting 1/x = p and 1/y = q in (i) and (ii) we get,

6q + 3p - 6 = 0

2q + 4p - 5 = 0

By cross multiplication method, we get

p/(-30-(-12)) = q/(-24-(-15)) = 1/(6-24)

p/-18 = q/-9 = 1/-18

p/-18 = 1/-18

p = 1 and q = 1/2

p = 1/x = 1 and q = 1/y = 1/2

x = 1, y = 2

Hence, x = 1 and y = 2

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 1.6 | Page 67