Question

Solve the following system of linear equation.

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

Answer 1

Answer:

Step-by-step explanation:

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

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

Substracting (2) from (1) we get

-2bx = -2ab - -2b2

x = a + b

Subsitute x in equation (2) we get

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

Answer 2

Answer:

The given expression may be written as

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

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

Subtracting eq.1 from eq.2,we get

{(a+b)x+(a+b)}=. 2ab+2b^2.

Or 2bx=2b(a+b)

Or x=2b(a+b)/2b

x=(a+b)

Putting x=(a+b) in eq.2 ,we get

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

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

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

Or(a+b)y=-2ab

y=-2ab/a+b

Hence x= (a+b) and y=-2ab/a+b is required solution.