Question

Solve for x and y:

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

( a + b)( x + y ) = a^2 + b^2

Answer 1

Answer:

x = a + b

y = - 2 ab / ( a + b )

Step-by-step explanation:

Given :

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

Also :

( a + b )( x + y ) = a² + b²

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

Subtract ( 2 ) from ( 1 ) to get :

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

= > ( a - b ) x - ( a + b ) x = - 2 ab - 2 b²

= > a x - b x - a x - b x = - 2 ab - 2 b²

= > - 2 bx = - 2 ab - 2 b²

= > - 2 bx = - 2 b ( a + b )

= >  x =  ( a + b )

Solve for y in the equation 2 :

( a + b ) x + ( a + b ) y = a² + b²

= > ( a + b ) ( a + b )  + ( a + b ) y = a² + b²

= > ( a + b )²  + ( a + b ) y = a² + b²

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

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

= > ( a + b ) y = - 2 ab

= > y = - 2 ab / ( a + b )