Question

solve for x and y. ax/y + by/a = a+b, ax - by= 2ab.​

Answer 1

Answer:

ax - by = 2ab … (2)

Multiplying by ab to (1) and a to (2), we get

a²x – b²y = a²b + ab²… (3)

a²x – aby = 2a2b … (4)

Subtracting equation (4) from equation (3),

(a²x – a²x) + ( - aby) – ( - b²y) = (2a²b - a²b) – ab²

⇒ - aby + b²y = a²b – ab²

⇒ by(b – a) = ab(a – b)

⇒ y = b(b – a) / ab(a – b)

⇒ y = - a

Substitute y value in (2),

ax – b( - a) = 2ab

⇒ ax + ab = 2ab

⇒ ax = ab

⇒ x = b

Answer 2

Step-by-step explanation:

ax/y + by/a = a+b -----> eq(1)

ax - by= 2ab -----> eq(2)

from equation (2)/y :

ax/y - b = 2ab/y

ax/y = (2ab/y)+ b

from equation (1)

2ab/y + b + by/a = a+b

2ab/y + by/a = a

2a^2.b + by^2 = a^2 y

by^2 - a^2 y + 2a^2.b = 0

y 1 = a^2 + √a^4-8a^2.b^2 / 2b

y 2 = a^2 - √a^4-8a^2.b^2 / 2b

from equation 2 :

x = 2b+(by/a)

x = 2b + b(a^2 + √a^4-8a^2.b^2 / 2b)/a

x 1 = b(a+√a^2-8b^2 +2 )

x 2 = b(a-√a^2-8b^2 +2 )