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# Solve for x and y : ax/b–by/a=a+b; ax–by=2ab - Mathematics

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Sum

Solve for x and y : \frac { ax }{ b } – \frac { by }{ a } = a + b ; ax – by = 2ab

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#### Solution

The given system of equations is

\frac { ax }{ b } – \frac { by }{ a } = a + b ….(1)

ax – by = 2ab ….(2)

Dividing (2) by a, we get

x – \frac { by }{ a } = 2b ….(3)

On subtracting (3) from (1), we get

\frac { ax }{ b } – x = a – b ⇒ x( \frac{a}{b}-1) = a – b

⇒ x = \frac{(a-b)b}{a-b} = b ⇒ x = b

On substituting the value of x in (3), we get

b  – \frac { by }{ a } = 2b ⇒ b( 1-\frac{y}{a}) = 2b

⇒ 1 – \frac { y }{ a } = 2 ⇒ \frac { y }{ a } = 1 – 2

⇒ \frac { y }{ a } = –1 ⇒ y = –a

Hence, the solution of the equations is x = b, y = – a

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method
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