Question

Solve by cross multiplication (a-b)x + (a+b)y= 2a²-2b² (a+b) (x+y) = 4ab

Plz fast!

Answer 1

Given:
(a-b)x+(a+b)y = 2a2+2b2 ------------(1), (a+b)x-(a-b)y = 4ab -----------(2)
multiply (a+b) in equation (1) and (a-b) in equation (2) we get
(a-b)(a+b)x + (a+b)2y = 2(a2+b2 )(a+b)
(a-b)(a+b)x -  (a-b)2y = 4ab(a-b)         (subtract)       
---------------------------------------------------------
                2(a2+b2 )y = 2a3 +2a2b+2ab2+2b3 -4a2b+4ab2
                            y = (2a3 +2b3 -2a2b+6ab2 ) / 2(a2+b2 )
                            y = 2(a3 +b3 -a2b+3ab2 ) / 2(a2+b2 )
                            y = (a3 +b3 -a2b+3ab2 ) / (a2+b2 )
multiply (a-b) in equation (1) and (a+b) in equation (2) we get
     (a-b)2x + (a+b)(a-b)y = 2(a2+b2 )(a-b)
     (a+b)2x -  (a-b)(a+b)y = 4ab(a+b)          (adding)    
     ---------------------------------------------------------
2(a2+b2 ) x = 2a3 - 2a2b+2ab2 -2b3+4a2b+4ab2
2(a2+b2 ) x = 2a3 + 2a2b+6ab2 -2b3
x = 2(a3 + a2b+3ab2 -b3 ) / 2(a2+b2 ) 
 ∴ x = (a3 + a2b+3ab2 -b3 ) / (a2+b2 )  ,y = (a3 +b3 -a2b+3ab2 ) / (a2+b2 )

Answer 2

Answer:

Given:

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

(a+b)x-(a-b)y=4ab-----------(2) multiply (a+b) in equation (1) and (a-b) in equation (2) we get (a-b)(a+b)x+ (a+b)2y = 2(a2+b2 )(a+b) (a-b)(a+b)x - (a-b)2y = 4ab(a-b) (subtract)

2(a2+b2 )y=

2a3+2a2b+2ab2+2b3 -4a2b+4ab2 y =

(2a3 +2b3-2a2b+6ab2 ) / 2(a2+b2)

y = 2(a3 +b3-a2b+3ab2 ) / 2(a2+b2) y = (a3 +b3 -a2b+3ab2 ) /

(a2+b2)

multiply (a-b) in equation (1) and (a+b) in equation (2) we get

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

(a+b)2x - (a-b)(a+b)y = 4ab(a+b)

(adding)

2(a2+b2 ) x = 2a3 -

2a2b+2ab2-2b3+4a2b+4ab2 2(a2+b2 ) x = 2a3 + 2a2b+6ab2 -2b3 x = 2(a3 + a2b+3ab2 -b3) / 2(a2+b2)

..x = (a3 + a2b+3ab2 -b3 ) / (a2+b2) y = (a3 +b3 -a2b+3ab2 ) / (a2+b2)