Question

What are the values of x and y if
x+y=a+b
ax-by=a^2-b^2?

Answer 1

Answer:

As x + y = a + b, and

$ax - by = a^2 - b^2$

$\Rightarrow ax - by = (a+b)(a-b)\\\Rightarrow ax - by = (x + y) (a-b) [\because x + y = a + b]$

Solving, we get

$ay-bx=0$    ...(1)

Now, multiply given equation with $\text {a}$,

Now, given equation becomes as

$ax+ay=a^2+ab$      ...(2)

Solving Eqns. (1) and (2), we get

$x = a \text { and } y = b$

Step-by-step explanation: