Answer :

We have,

ax – by = a2 + b2 …(i)


x + y = 2a …(ii)


To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.


Lets multiply equation (ii) by b, so that variable y in both the equations have same coefficient.


Recalling equations (i) & (ii),


ax – by = a2 + b2


x + y = 2a [×b



ax + bx = a2 + b2 + 2ab


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


x = a + b


Substitute x = (a + b) in equations (i)/(ii), as per convenience of solving.


Thus, substituting in equation (ii), we get


a + b + y = 2a


y = 2a – a – b


y = a – b


Hence, we have x = (a + b) and y = (a – b).


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