An important and exam oriented question from linear equations in two variables in which we have been asked to find the value of variables x and y from the given equations 3(2x+y)=7xy, 3(x+3y)=11xy

Kindly solve the above equations

RS Aggarwal, Class 10, chapter 3B, question no 39

Given:3(2x+y)=7xy,3(x+3y)=11xy

Divide both sides byÂ xy

(6x+3yâ€‹)/xy=7, (3x+9yâ€‹)/xy=11

6/y+3/x=7, 3/y+9/xâ€‹=11

LetÂ u=1/xâ€‹, v=1/yÂ then the above equations becomes

6v+3u=7Â Â Â Â ……(1)Â and

3v+9u=11Â Â ….(2)

Eqn(1)âˆ’2Ã—(2)

â‡’6v+3uâˆ’6vâˆ’18u=7âˆ’22

â‡’âˆ’15u=âˆ’15Â orÂ u=1

Substitute the value ofÂ u=1Â in eqn(1)Â we get

6v+3u=7

orÂ 6v=7âˆ’3=4

orÂ v=32â€‹

From above we have

u=1/xâ€‹

â‡’x=1/uâ€‹=1

andÂ v=1â€‹/y

â‡’y=1/vâ€‹

Â Â Â =â€‹3/2

âˆ´x=1, y=3/2