Solve the given pair of linear equations:
$(a - b) x + (a + b) y = a^{2} - 2 a b - b^{2}$
$(a + b) (x + y) = a^{2} + b^{2}$

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Solution

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

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Solve the following pair of linear equation:

(a - b)x + (a + b)y = a² - 2ab - b²

( a + b)(x + y)= a² +b²

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

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

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

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

x

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\begin{matrix} (a - b) x + (a + b) y = a^{2} - 2 a b - b^{2} (a + b) (x + y) = a^{2} + b^{2} \end{matrix}

x

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

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

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