Let x/a + y/b = 2 ··· Eq.1, and ax - by = a² - b² ··· Eq.2
Multiply Eq.1 by a²b, and Eq.2 by b. Eq.1 and Eq.2 can be rewritten as follows, respectively:
abx + a²y = 2a²b ··· Eq.3,
abx - b²y = a²b - b³ ··· Eq.4 Subtract Eq.4 from Eq.3.
(a² + b²)y = 2a²b - (a²b - b³) ⇒ (a² + b²)y = a²b + b³ ⇒ (a² + b²)y = (a² + b²)b We have: y = b
Plug y = b into Eq.1 x/a + b/b = 2 ⇒ x/a + 1 = 2 ⇒ x/a = 1 We have: x = a
CK: Plug x = a and y = b into LHS of Eq.2. LHS = ax - by = a² - b², while RHS = a² - b²,
so LHS = RHS CKD.
The answer is: x = a, and y = b **
** I still don't know if this question is a math problem or just a quiz for guessing sort of. When I saw the 1st equation, the sum of 2 numbers makes 2, the first thing came to my head is 1+1=2, so x=a, and y=b came instantly. I moved them into the 2nd equation. a·a-b·b=a²-b². Since these are linear functions, so any other answers don't exist other than x=a, and y=b. Done.