Answer :

We have,

⇒ bx + ay = 2ab …(i)

ax – by = a^{2} – b^{2}…(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 = a^{2} – b^{2} [×a

⇒ b^{2}x + a^{2}x = 2ab^{2} + a^{3} – ab^{2}

⇒ (b^{2} + a^{2})x = a (2b^{2} + a^{2} – b^{2})

⇒ (b^{2} + a^{2})x = a(b^{2} + a^{2})

⇒ 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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