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 by xy
(6x+3y)/xy=7, (3x+9y)/xy=11
6/y+3/x=7, 3/y+9/x=11
Let u=1/x, v=1/y then the above equations becomes
6v+3u=7 ……(1) and
3v+9u=11 ….(2)
Eqn(1)−2×(2)
⇒6v+3u−6v−18u=7−22
⇒−15u=−15 or u=1
Substitute the value of u=1 in eqn(1) we get
6v+3u=7
or 6v=7−3=4
or v=32
From above we have
u=1/x
⇒x=1/u=1
and v=1/y
⇒y=1/v
=3/2
∴x=1, y=3/2