Question

solve the following systems of linear equations: a (x+y) + b (x-y) = a square - ab + b square a (x+y) - b (x-y) = a square + ab + b square​

Answer 1

Given:

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

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

To find,

The values of x and y.

_________________________________________

Adding both the equations,

We get,

=> a(x + y) + b(x - y) + a(x + y) - b(x - y) = a² - ab + b² + a² +ab - b²

=> 2a(x + y) = 2a²

=> x + y = a ...(iii),

____________________

Subtracting (ii) from (i),

=> a(x + y) + b(x - y) -(a(x + y) - b(x - y)) = a² - ab + b² - (a² + ab -b²)

=> a(x + y) + b(x - y) - a(x - y) + b(x - y) = a² - ab + b² - a² - ab + b²

=> 2b(x - y) = -2ab + 2b²

=> 2b(x - y) = 2b² - 2ab

=> 2b(x - y) = 2b(b - a)

=> x - y = b - a ..(iv)

_______________________

Adding (iii) & (iv),

We get,

=> (x + y) + (x - y) a + b- a

=> 2x = b

=> x = b/2

substitute value of x in (iv)

y= a - b/2

Hope This Will Help you

Please mark me as Brainliest

Thank you