Question

if find x and y.......​

Answer 1

Step-by-step explanation:

Given -

x + y = a + b

ax - by = a² - b²

To Find -

• Value of x and y

By Elimination method :-

→ [ x + y = a + b ] × b

[ ax - by = a² - b² ] × 1

→ xb + yb = ab + b²

ax - by = a² - b²

______________

→ x(a + b) = a(a + b)

→ x = a

Now, Substituting the value of x on x + y = a + b, we get :

→ x + y = a + b

→ a + y = a + b

→ y = b

Hence,

The value of x is a and value of y is b

Verification :-

• x + y = a + b

→ a + b = a + b

LHS = RHS

And

• ax - by = a² - b²

→ a×(a) - b×(b) = a² - b²

→ a² - b² = a² - b²

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.

Answer 2

Step-by-step explanation:

Given that:-

$x + y = a + b \\ ax - by = {a}^{2} - {b}^{2}$

Solution:-

multiplying a in equation (1)

ax+ay=a×a+a×b -------------------(1)

$= > ax + ay = {a}^{2} + ab$

By elemination method:-

$ax + ay = {a}^{2} + ab \\ ax - by = {a}^{2} - {b}^{2}$

Eq(1)-(2)

$= > ay - by = ba - {b}^{2} \\ = > y(a - b) = b(a - b) \\ = > y = b( \frac{a - b}{a - b} ) \\ = > y = b \\ subsitute \: value \: of \: y \: i n \: equation \: 2 \\ \: \: \: ax - by = {a}^{2} - {b}^{2} \\ = > ax - b \times b = {a}^{2} - {b}^{2} \\ = > ax - {b}^{2} = {a}^{2} - {b}^{2} \\ = > ax = {a}^{2} - {b}^{2} + {b}^{2} \\ = > ax = {a}^{2} \\ = > x = \frac{ {a}^{2} }{a} \\ = > x = a$

Now

x=a and y=b