Question

solve for x and y :- b/ a x+ a/b y = a2+b2, x+y = 2ab

Answer 1

b/ax+a/by=a+be eq-1
x+y=2ab eq-2
from eq-1
b²x+a²y/ab=a²+b²
b²x+a²y=a³b+b³a
b²x-b³a=a³b-a²y
b²(x-ba)=a²(b-ay)
frm eq 2 ... b2 ( x - x/2 + y/2 ) = a2 ( x/2 + y/2 - y )

-> b2 ( x/2 - y/2 ) = a2 ( x/2 - y/2 )

-> b2x - b2y = a2x - a2y

-> x ( b2 - a2 ) = y ( b2 - a2 )

-> x = y ..

Answer 2

Answer:

x = ab, y = ab

Step-by-step explanation

(b/a)x + (a/b)y = a² + b² ----- Equation 1

x + y = 2ab ----- Equation 2

Now, multiply Eq. 2 by (a/b)

(b/a)x + (a/b)y = a² + b²

- (a/b)x + (a/b)y = 2a²

---------------------------------

(b/a - a/b)x = -a² + b²

[(b² - a²)/ab]x = -a² + b²

x = -a² + b² × ab/(b² - a²) = ab

∴ x = ab

ab + y = 2ab

y = 2ab - ab = ab

∴ y = ab