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

Sum

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

#### 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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