Question

Solve
for x
and y
(a - b) x + (a+b)y= a² - 2ab-b²
(a+b)(x+y) = a^2 +b²​

Answer 1

Answer:

x=a+b, y=-2ab/a+b

Step-by-step explanation:

How do you solve (a-b) x + (a + b) y = a² - 2ab - b² , (a + b) (x + y) = a² + b²?

Franklin Templeton™.

Ruchi Chhabra

Answered 1 year ago

(a-b) x + (a + b) y = a² - 2ab - b²…………(1)

(a + b) (x + y) = a² + b²……………………(2)

Equation (2) can be written as (a + b)x+ (a+b) y = a² + b²………….(3)

Now we have to solve equation (1) and (3)

(a-b) x + (a + b) y = a² - 2ab - b²,…………(1)

(a + b)x+ (a+b) y = a² + b²………….(3)

Subtracting equation (3) from (1) we get

(a-b-a-b) x = a² - 2ab - b²- a² - b²

-2b x = - 2ab -2 b²

-2b x =-2b(a+b)

dividing both sides by -2b

x = a+b

Now substitude x=a+b in equation (1) we get

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

a² - b² + + (a + b) y = a² - 2ab - b²

Subtracting a² - b² from both the sides

(a + b) y = a² - 2ab - b² - a² + b²

(a + b) y = - 2ab

y = - 2ab /(a+b)

Answer x = a+b , y = - 2ab /(a+b)