Question

solve for x and y

please solve it urgently​

Answer 1

x - y =a +b

ax +by = a² - b²

    x/ -a²-ab+b²-b² = y/a²+ab-a²+b² = -1/-a-b

x/ -a²-ab =1/ a+b

x = -a(a + b)/a+b

x = -a

y/b²+ab = 1/a +b

y = b(a+b)/a+b

y =b

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

$x + y = a + b.........(1)$

$ax - by = {a}^{2} - {b}^{2} \: \: .......(2)$

TO DETERMINE

The value of x & y

CALCULATION

BY CROSS MULTIPLICATION RULE WE GET

$\displaystyle \: \: \frac{x}{( {a}^{2} - {b}^{2}) + b(a + b) } = \frac{y}{a(a + b) - ( {a}^{2} - {b}^{2} )} = \frac{1}{ b + a}$

$\implies \: \displaystyle \: \: \frac{x}{( {a}^{2} - {b}^{2} + ba + {b}^{2} ) } = \frac{y}{({a}^{2} + ab- {a}^{2} + {b}^{2} )} = \frac{1}{ ( b + a)}$

$\implies \: \displaystyle \: \: \frac{x}{( {a}^{2} + ba ) } = \frac{y}{( ab + {b}^{2} )} = \frac{1}{ ( b + a)}$

$\implies \: \displaystyle \: \: \frac{x}{a( {a} + b) } = \frac{y}{b( a + {b} )} = \frac{1}{ ( a + b)}$

Now

$\displaystyle \: \: \frac{x}{a( {a} + b) } = \frac{1}{ ( a + b)} \: \: \: gives$

$\displaystyle \: \: \frac{x}{a}= 1$

$\therefore \: x \: = a$

Again

$\displaystyle \: \: \frac{y}{b( a + {b} )} = \frac{1}{ ( a + b)}$ gives

$\implies \: \displaystyle \: \ \frac{y}{b} = 1$

$\therefore \: y \: = b$

RESULT

So the required solution is

$x \: = a \: \: \: \: and \: \: \: y \: = b$