Question

a minus b into X + a + b into Y is equal to a square minus 2 a b minus b square A + B Into X + a + b into Y is equal to a square + b square

Answer 1

Answer:

Value of x is a + b and y is -2ab/(a+b).

Step-by-step explanation:

Given system of equation,

( a - b )x + ( a + b )y = a² - 2ab - b² ............................(1)

( a + b )x + ( a + b )y = a² + b² ..........................(2)

We need to solve for x and y.

We solve by elimination method.

Subtract (2) from (1),

( a - b )x + ( a + b )y - ( ( a + b )x + ( a + b )y ) = a² - 2ab - b²- ( a² + b² )

( a - b )x + ( a + b )y - ( a + b )x - ( a + b )y = a² - 2ab - b²- a² - b²

( a - b )x - ( a + b )x = - 2ab - 2b²

( a - b - a - b )x = -2b ( a + b )

( -2b )x = -2b( a + b )

x = -2b( a + b ) / (-2b)

x = a + b

put this value in (1),

( a - b )( a + b ) + ( a + b )y = a² - 2ab - b²

a² - b² + ( a + b )y = a² - 2ab - b²

( a + b )y = a² - 2ab - b² - a² + b²  

( a + b )y = -2ab

y = -2ab/(a+b)

Therefore, Value of x is a + b and y is -2ab/(a+b).

Answer 2

Answer:

$x = a+b\\y= \frac{-2ab}{a+b}$

Step-by-step explanation:

Given

(a-b)x+(a+b)y=a²-2ab-b² --(1)

(a+b)x+(a+b)y=a²+b² -----(2)

/* Subtract equation (1) from equation (2), we get

(a+b)x-(a-b)x=a²+b²-(a²-2ab-b²)

=> [a+b-(a-b)]x=a²+b²-a²+2ab+b²

=> (a+b-a+b)x=2b²+2ab

=> 2bx= 2b(b+a)

$\implies x =\frac{2b(b+a)}{2b}\\=a+b\:--(3)$

Substitute x = a+b in equation (1) ,we get

$\implies (a-b)(a+b)+(a+b)y= a^{2}-2ab-b^{2}$

$\implies a^{2}-b^{2}+(a+b)y=a^{2}-2ab-b^{2}$

$\implies (a+b)y=a^{2}-2ab-b^{2}-a^{2}+b^{2}$

$\implies (a+b)y = -2ab$

$\implies y = \frac{-2ab}{a+b}$

Therefore,

$x = a+b\\y= \frac{-2ab}{a+b}$

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