This is the basic and exam oriented question from linear equations in two variables in which we have given two equations bx/a+ay/b=a²+b², x+y=2ab and we have to find the value of variables x and y from the equations
Kindly solve the above equations
RS Aggarwal, Class 10, Chapter 3B, question no 47
Given equation are
bx/a+ay/b=a²+b² ….(i)
x+y=2ab….(ii)
eqn(i) can be written as,
⇒bx/a+ay/b=a²+b²
⇒b²x+a²y=ab×(a²+b²)
⇒x=(ab×(a²+b²)−a²y)/b²….(iii)
Now from eqn (ii), y = 2ab – x…(iv)
On substituting y = 2ab – x in eqn (iii), we get
⇒x=(a³b+b³a−2a²b+a²x)/b²
⇒b²x=b³a−a³b+a²x
⇒b²x−a²x=b³a−a³b
⇒(b²−a²)x=ab(b²−a²)
⇒x=ab
Now putting x = ab in eqn (iv) we get
⇒y=2ab−ab
⇒y=ab
Thus, x=ab and y=ab is the required solution