Question

If x+y=a-b and ax-by=a²+b² find the value of x and y *

Answer 1

Answer:

The answer is $(a,-b)$

Step-by-step explanation:

Given       $x+y=a-b$.. (1) x $b$

and         $ax-by=a^2+b^2$...(2)

Multiply (1) by $b$ and add these equations

$\Rightarrow bx+by+ax-by=ab-b^2+a^2+b^2\\\Rightarrow bx+ax=ab+a^2\\\Rightarrow (b+a)x=a(b+a)\\\Rightarrow x=\dfrac{a(b+a)}{b+a}=a$

Now using (1)

  $a-y=a-b\\\Rightarrow y=-b$

Hence the solution is $(x,y)=(a,-b)$