Question

solve for X and Y.........

Answer 1

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

( a + b ) ( x + y ) = a^2 + b^2. ... ( 'll )

equation ( l )

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

ax - bx + ay + by = a^2 - 2ab - b^2. ( lll )

equation ( 'll )

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

ax + bx + ay + by = a^2 + b^2. ... ( IV )

subtracting equation ( lV ) from ( III ) we get

- 2bx = -2ab - 2b^2

dividing by - 2

bx = ab + b^2

x = a + b

putting x = a + b in equation 1 we get

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

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

(a + b)y = - 2 ab

y = - 2ab / ( a + b )

y = - 2ab / x