Question

Solve the following pair of linear equation:

(a - b)x + (a + b)y = a² - 2ab - b²

( a + b)(x + y)= a² +b²

Answer 1

Consider the given equations

The second equation can be written as follows

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

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

Now subtract the two equations

we get
(a-b)x - (a+b)x =-2ab-2b^2
ax-bx-ax-bx =-2ab-2b^2

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

Taking -2b outside and cancelling it, we get

x=a+b

Now substitute the value of x in any of the two given equations, then we get

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

These are the required values for x and y