Solve the following system of equations.
$(a - b) x + (a + b) y = a^{2} - 2 a b - b^{2}$ , $(a + b) (x + y) = a^{2} + b^{2}$ .

a - b, - 2 a b

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a + b, - 2 a b

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a^{2} + b^{2}, \frac{- 2 a b}{a + b}

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a + b, \frac{- 2 a b}{a + b}

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Solution

The correct option is D $a + b, \frac{- 2 a b}{a + b}$
given $(a - b) x + (a + b) y = a^{2} - 2 a b - b^{2}$ is equation 1 and

$(a + b) (x + y) = a^{2} + b^{2}$ is equation 2 so on doing equation $1$

$e q u a t i o n$ 2 $i s x = a + b$ from this we can get

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

Hence option D is the correct answer.

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Similar questions

Q. Solve the following system of equation in

x

and

y

(a - b) x + (a + b) y = a^{2} - 2 a b - b^{2}

(a + b) (x + y) = a^{2} + b^{2}

Q. Find the equation of the straight line passing through the pair of points (a, b) and (a + b, a-b).

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

Find:
$(a + b + c) \times (a + b - c) =$

Simplify $\frac{a - b}{a} + \frac{a + b}{b}$

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Solve the following system of equations.(a−b)x+(a+b)y=a2−2ab−b2, (a+b)(x+y)=a2+b2.

The correct option is D a+b,−2aba+bgiven (a−b)x+(a+b)y=a2−2ab−b2 is equation 1 and (a+b)(x+y)=a2+b2 is equation 2 so on doing equation 1 equation 2 isx=a+b from this we can get y=−2aba+b Hence option D is the correct answer.

Solve the following system of equations.
$(a - b) x + (a + b) y = a^{2} - 2 a b - b^{2}$ , $(a + b) (x + y) = a^{2} + b^{2}$ .