Question

Ahola!!!

Class 10th

Reduce the following pair of equations into pair of linear equations and SOLVE them :-

Ques in pic..part (i)



All the best !!!​

Answer 1

Answer:

Required value of x is 1 / 2 and y is - 3 / 2 .

Step-by-step explanation:

Reducing the equation $\dfrac{2xy}{x+y}=\dfrac{3}{2}$ into pair of linear equations :

$\implies \dfrac{2xy}{x+y}=\dfrac{3}{2}\\\\\\\implies \dfrac{2 \times 2 }{3}=\dfrac{x+y}{xy}\\\\\\\implies \dfrac{4}{3}=\dfrac{x}{xy}+\dfrac{y}{xy}\\\\\\\implies \dfrac{4}{3}=\dfrac{1}{y}+\dfrac{1}{x}\quad\quad \bold{...(1)}$

Reducing the equation $\dfrac{xy}{2x-y}=\dfrac{-3}{10}$ into pair of linear equations :

$\dfrac{xy}{2x-y}=\dfrac{-3}{10}\\\\\\\implies \dfrac{10}{-3}=\dfrac{2x-y}{xy}\\\\\\\implies -\dfrac{10}{3}=\dfrac{2x}{xy}-\dfrac{y}{xy}\\\\\\\implies - \dfrac{10}{3}=\dfrac{2}{y}-\dfrac{1}{x}\quad\quad\bold{... (2)}$

Let 1 / x = a and 1 / y = b.

= > 4 / 3 = a + b { equation 1 }

= > 4 = 3a + 3b

= > 4 - 3b = 3a ... ( 3 )

= > - 10 / 3 = 2b - a { equation 2 }

= > - 10 = 6b - 3a

= > 3a = 6b + 10 ...( 4 )

Comparing ( 3 ) & ( 4 ) :

= > 4 - 3b = 6b + 10

= > 4 - 10 = 6b + 3b

= > - 6 = 9b

= > - 6 / 9 = b

= > - 2 / 3 = b { thus, y = 1 / ( - 2 / 3 ) = - 3 / 2 }

Thus,

= > 4 - 3b = 3a

= > 4 - 3( - 2 / 3 ) = 3a

= > 4 + 2 = 3a

= > 6 = 3a

= > 2 = a { thus, x = 1 / 2 }

Hence the required value of x is 1 / 2 and y is - 3 / 2 .

Answer 2

Linear Equations :

Answer :

x = 1/2 and y = - 3/2

Explanation :

Refer the attached picture.