Find the values of $(x + y)$ and $(x - y)$ without actually solving for $x$ and $y$ . $8 x - 7 y = 11; 7 x - 8 y = 4$

x + y = 2, x - y = 1

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x + y = 1, x - y = 1

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x + y = 7, x - y = 1

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x + y = 3, x - y = 1

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Solution

The correct option is C $x + y = 7, x - y = 1$
Rewriting the given equations, we get

$8 x - 7 y = 11$ ...(i)
$7 x - 8 y = 4$ ...(ii)
On adding (i) and (ii) , we get
$15 x - 15 y = 15$
$\Rightarrow x - y = 1$
On subtracting (ii) from (i), we get
$x + y = 7$

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