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Solve (a – b) x + (a + b) y = a^2 – 2ab – b^2 (a + b) (x + y) = a^2 + b^2 - Mathematics

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Sum

Solve (a – b) x + (a + b) y = `a^2 – 2ab – b^2 (a + b) (x + y) = a^2 + b^2`

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Solution

The given system of equation is

`(a – b) x + (a + b) y = a^2 – 2ab – b^2 ….(1)`

`(a + b) (x + y) = a^2 + b^2 ….(2)`

`⇒ (a + b) x + (a + b) y = a^2 + b^2 ….(3)`

Subtracting equation (3) from equation (1), we get

`(a – b) x – (a + b) x = (a^2 – 2ab– b^2 ) – (a^2 + b^2 )`

`⇒ –2bx = – 2ab – 2b^2`

`⇒x=(-2ab)/(-2b)-(2b^2)/(-2b) = a + b`

Putting the value of x in (1), we get

`⇒ (a – b) (a + b) + (a + b) y = a^2 – 2ab – b^2`

`⇒ (a + b) y = a^2 – 2ab – b^2 – (a^2 – b^2 )`

⇒ (a + b) y = – 2ab

`⇒ y = \frac { -2ab }{ a+b }`

Hence, the solution is x = a + b,

`y = \frac { -2ab }{ a+b }`

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