# Solve the following pairs of equations by reducing them to a pair of linear equations 4/x + 3y = 14, 3/x - 4y = 23 - Mathematics

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

4/x + 3y = 14

3/x - 4y = 23

#### Solution

4/x + 3y = 14

3/x - 4y = 23

Putting 1/x = p in the given equations, we get

4p + 3y = 14 ⇒ 4p + 3y - 14 = 0

3p - 4y = 23 ⇒ 3p - 4y -23 = 0

By cross-multiplication, we get

p/(-69-56) = y/(-42-(-92)) = 1/(-16-9)

⇒ (-p)/125 = y/50 = (-1)/25

Now,

(-p)/125 = (-1)/25 and y/50 = (-1)/25

⇒ p = 5 and y = -2

Also, p = 1/x = 5

⇒ x = 1/5

So, x = 1/5 and y = -2 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 1.3 | Page 67