Solve for x and y:

ax + by = (a2 + b2)

We have,


bx – ay = 0 …(i)


ax + by = a2 + b2…(ii)


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


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


Recalling equations 1 & 2,


bx – ay = 0 [×b


ax + by = a2 + b2 [×a



b2x + a2x = a3 + ab2


(b2 + a2)x = a (a2 + b2)


(b2 + a2)x = a(b2 + a2)


x = a


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


Thus, substituting in equation (i), we get


ab – ay = 0


ay = ab


y = b


Hence, we have x = a and y = b.


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