Question

x/a + y/b = 2
ax-by=a^2-b^2
Solve for x and y

Answer 1

Solutions :-

We have,
x/a + y/b = 2
ay + xb = 2ab _____(i)
ax - by = a² - b² ____(ii)

Now,
From equation (i) and (ii)
Multiply (i) by 'a' (ii) by 'b'

abx + a²y = 2a²b
abx - b²y = ba² - b³
y(a² + b²) = 2a²b - ba² + b³
y(a² + b²) = a²b + b³
y(a² + b²) = b(a² + b²)

y = b

{Put in equation (i)}. we get,
=> ay + xb = 2ab
=> a(b) + xb = 2ab
=> xb = 2ab - ab
=> x = ab/b
=> x = a


Answer : y = b
x = a