Question

x+y=a+b...ax-by=asquare + bsquare​

Answer 1

Answer:

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Answer 2

Answer:

The solution of the equations is x=a and y=b.

Method :

Given : Equations $x+y=a+b$ and $ax-by=a^2-b^2$

To find : Solve the equations?

Solution :

Let  $x+y=a+b$.......(1)

and  $ax-by=a^2-b^2$......(2)

Substitute x from (1) in equation (2),

$a(a+b-y)-by=a^2-b^2$

$a^2+ab-ay-by=a^2-b^2$

$ab-(a+b)y=-b^2$

$ab+b^2=(a+b)y$

$b(a+b)=(a+b)y$

$y=b$

Substitute y in equation (1),

$x+b=a+b$

$x=a+b-b$

$x=a$

Therefore, The solution of the equations is x=a and y=b.