# Solve for x and y

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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