Question

Math's genius solve this if you can

Answer 1

ax+by=a−b⋯(1)ax+by=a−b⋯(1)
bx−ay=a+b⋯(2)bx−ay=a+b⋯(2)
(1)×a⟹a2x+aby=a2−ab⋯(3)(1)×a⟹a2x+aby=a2−ab⋯(3)
(2)×b⟹b2x−aby=ab+b2⋯(4)(2)×b⟹b2x−aby=ab+b2⋯(4)
Adding the like terms of both equations,
(a2+b2)x=a2−ab+ab+b2(a2+b2)x=a2−ab+ab+b2
⟹(a2+b2)x=a2+b2⟹(a2+b2)x=a2+b2
[∵+aby and -aby gets cancelled∵+aby and -aby gets cancelled]
⟹x=a2+b2a2+b2⟹x=a2+b2a2+b2
⟹x=1⟹x=1
Substitute x=1 in equation (1).
a(1)+by=a−ba(1)+by=a−b
a+by

Therefore, solution is (x,y)=(1,−1)