Question

x/a + y/b =a+b and x/a^2 + y/b^2 =2

Answer 1

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Given (x/a) + (y/b) = a + b Multiply by (1/a) both sides, we get (x/a2) + (y/ab) = 1 + (b/a) → (1) Given other linear equation as (x/a2) + (y/b2) = 2  → (2) Subtract (2) from (1), we get (x/a2) + (y/ab) = 1 + (b/a)(x/a2) + (y/b2) = 2  ----------------------------------(y/ab) − (y/b2) = (b/a) − 1 ⇒ y[(b − a)/ab2] = (b − a)/a ∴ y = b2 Put y = b2 in (x/a2) + (y/b2) = 2  ⇒ (x/a2) + (b2/b2) = 2  ⇒ (x/a2) + 1 = 2  ⇒ (x/a2)  = 1 ∴ x = a2