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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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