Question

Solve Q.3.
chapter - Linear equations in two variables

Answer 1

let 1/x be p and 1/y be
therefore equations become
ap-bq=0
and
ab^2+a^b=(a^2+b^2)

now using cross multiplication we get-

p/a^2b+b^3=q/a^3+ab^2 = 1/a^3b+ab^3
p/(a²+b²) b = q/(a²+b²)a= 1/ab(a²+b²)

on equating we get.
p= 1/ab and q=1/ab

1/x =1/ab
therefore x= ab
1/y = 1/ab
therefore y = ab.

Answer 2

Answer:

x = a

y = b

Step-by-step explanation:

Let 1 / x be p .

Let 1 / y be q .

a p - b q= 0 ............( 1 )

ab² p + a²b q  = ( a² + b² )

⇒ ab² p+ a²b q - ( a² + b² ) = 0 ...........( 2 )

Comparing those with normal simultaneous equation :

a₁ = a

a₂ = ab²

b₁ = - b

b₂ = a²b

c₁ = 0

c₂ = - ( a² + b² )

By cross multiplication method :

x / ( b₁c₂ - b₂c₁ ) = 1 / ( a₁b₂ - a₂b₁ )

= > p / ( ( - b )(-( a² + b² )) - 0 ) = 1 / ( a ( a² b ) - ( - b )( ab² )

= > p / ( a² b+ b³ ) =  1 / ( a³ b + a b³ )

= > p / b ( a² + b² )  = 1 / ab( a² + b² )

= > p / b = 1 / ab

= > p = 1 / a

1 / x = p

So 1 / x = 1 / a

= > x = a

y / ( a₂c₁ - a₁c₂ ) = 1 / ( a₁b₂ - a₂b₁ )

= > q / ( ab² . 0 + a ( a² + b² ) )- 1 / ( a ( a² b ) - ( - b )( ab² )

= > q / a ( a² + b² ) = 1 / ( a³b + ab³ )

= > q / a ( a² + b² ) = 1 / ab ( a² + b² )

= > q / a = 1 / ab

= > q = 1 / b

1 / y = q

= > 1 / y = 1 / b

= > y = b