Question

If bx+ay=a²+b² and ax-by=0, the value of x-y is ?​

Answer 1

Given ax+by=a^2-b^2 ; bx+ay=0

then x+y=?

Adding given equations

ax+by+bx+ay=a^2-b^2

(a+b)x+(a+b)y=a^2-b^2

(a+b)(x+y)=a^2-b^2

(a+b)(x+y)=(a+b)(a-b)

x+y=a-b

Answer 2

Answer:

x - y = b - a

Step-by-step explanation:

Given :

bx + ay = a² + b²

ax - by = 0  

Then, to find the value of (x - y)

Solution :

bx + ay = a² + b² ..(i)

ax - by = 0  ..(ii)

By adding (i) × b and (ii) × a ,

We get,

[ (i) × b ] + [ (ii) × a ] ⇒ b(bx + ay) + a(ax - by) = b(a² + b²) + a(o)

⇒ b²x + aby + a²x - aby = b(a² + b²)

⇒ a²x + b²x = b(a² + b²)

⇒ x(a² + b²) = b(a² + b²)

⇒ x = b ...(iii)

Substituting value of x in (ii),

We get,

⇒ a(b) - by = 0

⇒ -by = - ab

⇒ by = ab

⇒ y = a ..(iv)

By subtracting (iv) from (iii),

We get,

x - y = b - a

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