Solve by any method

x/a-y/b=a-b

x/a^2-y/b^2=0

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Solution

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) = 0 → (2)
Subtract (2) from (1), we get
(x/a²) - (y/ab) = 1 -(b/a)
(x/a²) - (y/b²) = 0
----------------------------------
-(y/ab) + (y/b²) = 1 - (b/a)
⇒ y[(-b + a)/ab²] = ( a - b)/a
∴ y = b²
Put y = b² in (x/a²) - (y/b²) = 0
⇒ (x/a²) - (b²/b²) = 0
⇒ (x/a²) - 1 = 0
⇒ (x/a²) = 1
∴ x = a²
x = a^{2
and}y = b²

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