Question

Solve for x and y x + y equals to a + b and a x minus b y equals to a square minus b square

Answer 1

Answer:

x = a, y = b.

Step-by-step explanation:

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

$ax - by = a^2 - b^2 = (a - b)(a + b)$ (given, identity)

$ax - by = (a - b)(x + y)$ (replacing from given equation)

$ax - by = ax + ay - bx - by$ (opening the brackets)

$ax - ax - by + by = ay - bx$ (shifting terms)

$0 = ay - bx$

=> $ay = bx$

Multiplying first given equation by a, we get:

$ax + ay = a^2 + ab$

Substituting $ay = bx$, we get:

$ax + bx = a(a + b)$

$x(a + b) = a(a + b)$

$x = a$

Now, $ay = bx$

So, $ay = ba$

Or, $y = b$

Answer 2

Answer:x = a, y = b.

Step-by-step explanation:

(given)

(given, identity)

(replacing from given equation)

(opening the brackets)

(shifting terms)

=>  

Multiplying first given equation by a, we get:

Substituting , we get:

Now,  

So,  

Or,

Step-by-step explanation: