Solve for $x & y$ ;
$x + y = a + b$
$a x - b y = a^{2} - b^{2}$

x = - a, y = b

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x = a, y = b

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x = a, y = - b

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None of these

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Solution

The correct option is C $x = a, y = b$
$a (x + y) = a (a + b) \Rightarrow a x + a y = a^{2} + a b . . . . . . . . . (1)$

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

$(1) - (2)$ gives
$(a + b) y = b (a + b) \Rightarrow y = b$

Hence, From (1) $x = a$

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Solve for x and y:

$\frac{x}{a} + \frac{y}{b} = 2, a x - b y = a^{2} - b^{2} .$

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