Question

Solve for x and y: bx+ay=2ab ax-by=a^2-b^2

Answer 1

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x=ay=b

Answer 2

Answer:

Given equations can be written as

bx + ay - 2ab = 0

and ax - by - a2+b2=0

By cross multiplication method, we have

xa×[−(a2−b2)]−(−b)×(−2ab)=y(−2ab)×a−[−(a2−b2)]×b=1b×(−b)−a×a

⇒xa(−a2+b2−2ab2)=y−2a2b+a2b−b3=1−b2−a2

implies xa(−a2−b2)=y−a2b−b3=1−b2−a2

when xa(−a2−b2)=1−b2−a2

⇒x=−a(a2+b2)−1(b2+a2)orx=a

and y−a2b−b3=1−b2−a2

implies y=−b(a2+b2)−1(b2+a2)ory=b

Hence, x=ay=b} is the required solution.