Solve for x and y: x + y = a + b, a x-b y=a^2-b^2 - Vidyadip

Question

Solve for $x$ and $y$:
$x + y = a + b,$
$a x-b y=a^2-b^2$

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Answer

$x + y = a + b ...(i)$
$a x-b y=a^2-b^2...(ii)$
Multiplying $(i)$ by b adding it to $(ii)$, we get
$\Rightarrow bx + ax = ab + b^2 + a^2 - b^2$
$\Rightarrow x(a + b) = a(a + b)$
$\Rightarrow x = a$
Substitute $x = a$ in $(i)$, we get $y = b.$
So, $x = a$ and $y = b.$

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