NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(i)

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(i)

Question:

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?

Given:

Let the fraction be x y . Adding 1 to the numerator and subtracting 1 from the denominator gives 1. Adding 1 to the denominator gives 1 2 .

To Find:

The fraction x y .

Formula:

Elimination method for solving linear equations.

Solution:

From the given information, we can form two linear equations:

x+1 y-1 = 1 ⇒ x + 1 = y - 1 ⇒ x - y = -2 ...(1)

And,

x y+1 = 1 2 ⇒ 2x = y + 1 ⇒ 2x - y = 1 ...(2)

Subtracting (1) from (2):

(2x - y) - (x - y) = 1 - (-2) ⇒ x = 3

Substituting x = 3 in (1):

3 - y = -2 ⇒ y = 5

Result:

Therefore, the fraction is 3 5 .

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