Question

a fraction becomes 1/3 when 2 is subtracted from numerator and 1 is added to denominator” write a linear equation taking numerator and denominator as X and Y respectively
PLEASE WRITE IN EXPLANATION​

Answer 1

Let the numerator = x

Let the denominator = y

so, the fraction = xy

Now, it is given that when 2 is subtracted from the denominator and 3 is added to the denominator, then fraction reduces to 1/4.

So, according to given condition, we have

x − 2y + 3 = 14⇒4(x − 2) = y + 3⇒4x − 8 = y + 3⇒4x − y = 3 + 8⇒4x − y = 11 .....(1)

Put x = 3 in the (1), we get

4(3) - y = 11

⇒12 - y = 11

⇒- y = 11 - 12

⇒y = 1

so, (3, 1) is the solution of the equation.

Put x = 4 in (1), we get

4(4) - y = 11

⇒16 − y = 11⇒−y = 11 − 16⇒ −y = − 5⇒y = 5

so, (4, 5) is the solution of the equation

Answer 2

Step by step explanation

Given:

• A fraction becomes 1/3 when 2 is subtracted and 1 is added to its numerator & denominator respectively.

To Write:

• A linear equation taking numerator and denominator as x and y respectively.

Solution: Let the numerator be x and denominator be y. Therefore,

➟ Fraction will be = Numerator/Denominator

➟ Fraction = x/y

A/q

• Subtracting 2 from numerator

• New numerator = (x – 2)

• Adding 1 to denominator

• New denominator = (y + 1)

After this new fraction will be 1/3.

So the linear equation will be

➮ New numerator/new denominator = 1/3

➮ x – 2/y + 1 = 1/3

➮ 3(x – 2) = 1(y + 1)

➮ 3x – 6 = y + 1

➮ 3x – y = 1 + 6

➮ 3x – y = 7

➮ 3x – y – 7 = 0 (This is a linear equation in two variables)

Hence, it is the required linear equation.