Question

The circled question...........................

Answer 1

Answer:

let 1/x and 1/y be a and b

Step-by-step explanation:

so eqaution formed is

2a+3b=2

18a+12b=13

by elimination methord b=1/3 and a=1/2

hope you like by shortest trick

Answer 2

Answer:

x = 1/2 ; y = 1/3

Step-by-step explanation:

$\implies \dfrac{1}{2x} + \dfrac{1}{3y} = 2\\\\\text{Taking LCM we get,}\\\\\implies \dfrac{3y + 2x}{3y \times 2x} = 2\\\\\\\implies \dfrac{3y+2x}{6xy} = 2\\\\\implies 3y + 2x = 2 \times 6xy\\\\\implies 3y + 2x = 12xy \hspace{3mm} \rightarrow \text{Eqn 1}$

$\implies \dfrac{1}{3x} + \dfrac{1}{2y} = \dfrac{13}{6}\\\\\text{Taking LCM we get,}\\\\\implies \dfrac{2y + 3x}{2y \times 3x} = \dfrac{13}{6}\\\\\text{Cross multiplying we get,}\\\\\implies 6(2y + 3x) = 13(6xy)\\\\\text{ Cancelling the 6 on both sides we get,}\\\\\implies 2y + 3x = 13xy \hspace{3mm}\rightarrow \text{Eqn. 2}$

So Adding both the equations we get,

⇒ 3y + 2x + 2y + 3x = 12xy + 13xy

⇒ 5y + 5x = 25 xy

Dividing by common divisor 5 we get,

⇒ y + x = 5xy

⇒ y = 5xy - x    → Eqn. 3

Now subtracting the Eqn. 1 and Eqn. 2 we get,

⇒ 3y + 2x - ( 2y + 3x ) = 12xy - 13xy

⇒ 3y - 2y + 2x - 3x = -xy

⇒ y - x = -xy

Substituting value of y from Eqn. 3 we get,

⇒ 5xy - x - x = -xy

⇒ 5xy + xy = x + x

⇒ 6xy = 2x

Dividing by 2x on both sides we get,

⇒ 6xy / 2x = 2x / 2x

⇒ 3y = 1

⇒ y = 1/3

Hence value of y is 1/3.

Hence Substituting the value of 'y' in Eqn 3 we get,

⇒ 1/3 = 5x ( 1/3 ) - x

⇒ 1/3 = 5x/3 - x

Taking LCM on the LHS we get,

⇒ 1/3 = ( 5x - 3x ) / 3

⇒ 1/3 = 2x / 3

Cancelling out 3 we get,

⇒ 1 = 2x

⇒ x = 1/2

Hence the value of x is 1/2.