Question

Solve (a-b)x+(a+b)y=a² -2ab-b² ,(a+b)(x+y)=a² +b ²

Answer 1

Answer:

x = a + b

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

Step-by-step explanation:

Given :

To find the value of x & y if,

(a - b)x + (a + b)y = a² - 2ab - b²  ...(i)

(a + b)(x + y) = a² + b²

⇒ (a + b)x + (a + b)y = a² + b²   ...(ii)

Solution :

By subtracting (i) from (ii),

⇒ (ii) - (i)

⇒ [(a + b)x + (a + b)y] - [(a - b)x + (a + b)y] = [a² + b²] - [a² - 2ab - b²]

⇒ [(a + b) - (a - b)]x = 2ab + 2b²

⇒ (2b)x = 2b(a + b)

⇒ x = a + b ...(iii)

By substituting value of x in (i),

We get,

⇒ (a - b)x + (a + b)y = a² - 2ab - b²

⇒ (a - b)(a + b) + (a + b)y = a² - 2ab - b²

⇒ a² - b² + (a + b)y = a² - 2ab - b²

⇒ (a + b)y = a² - 2ab - b² - a² + b²

⇒ (a + b)y = -2ab

⇒ y = $\frac{-2ab}{a + b}$