Question

solve this eq with substitution method : (x/a) +(y/b) =2 & ax-by=a^2-b^2

Answer 1

x/a + y/b = 2    -------(1)
ax-by= a2 - b2  ------(2)

x/a = 2-y/b
x    = 2a - ay/b
substitute x in (2).
a(2a - ay/b) - by = a2 - b2
2a2 - a2y/b - by = a2 -b2
a2 - a2y/b -by+ b2 = 0
a2 +b2 = a2y/b + by
a2 + b2 = (a2y + b2y)/b
b(a2 + b2) = (a2 + b2)y
therefore, y = b

x/a +y/b =2  -----(1)
x/a +b/b =2
x/a =2-1
x = a
therefore x=a

So the answer is x=a and y=b

Answer 2

x/a + y/b = 2      
---(1) ax-by= a2 - b2  
----(2)x/a = 2-y/b x    
= 2a - ay/b substitute x in (2).
 a(2a - ay/b) - by
= a2 - b2 2a2 - a2y/b - by
= a2 -b2 a2 - a2y/b -by+ b2 
= 0 a2 +b2 = a2y/b + by a2 + b2
 = (a2y + b2y)/b b(a2 + b2) = (a2 + b2)y therefore,

y = b x/a +y/b =2  -----(1) 
x/a +b/b =2
 x/a =2-1
 x = a
therefore
x=a