Q. 414.5( 24 Votes )

Solve for x and y:

ax - by = a2 - b2.

Answer :

We have,


bx + ay = 2ab …(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 = 2ab [×b


ax – by = a2 – b2 [×a



b2x + a2x = 2ab2 + a3 – ab2


(b2 + a2)x = a (2b2 + 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 = 2ab


ay = 2ab – ab = ab


y = b


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


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