Solve for x and y:

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

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Solution

$x + y = a + b$ .....(1) $a x - b y = a^{2} - b^{2}$ ....(2)

multiplying by b in (1)

$a x + b y = a b + b^{2}$ ....(3)

subtracting equ (2) from (3)then we get

$x (a + b) = a (b + a)$
$x = a$
put the value of x in (1)

$x + y = a + b a + y = a + b y = b$

so x=a and y=b

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